Artifact 1598f07f8a9d8c6160b7780162cdf554b06a8118554edf46fabe2f41ada0c751:
- Executable file
r36/xlog/DEFINT.LOG
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 15137) [annotate] [blame] [check-ins using] [more...]
REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... *** ci already defined as operator *** si already defined as operator % Test cases for definite integration. int(x/(x+2),x,2,6); 2*( - log(2) + 2) int(sin x,x,0,pi/2); 1 int(log(x),x,1,5); 5*log(5) - 4 int((1+x**2/p**2)**(1/2),x,0,p); p*(sqrt(2) + log(sqrt(2) + 1)) -------------------------------- 2 int(x**9+y+y**x+x,x,0,2); 2 10*log(y)*y + 522*log(y) + 5*y - 5 ------------------------------------- 5*log(y) % Collected by Kerry Gaskell, ZIB, 1993/94. int(x^2*log(1+x),x,0,infinity); 2 int(x *log(1 + x),x,0,infinity) int(x*e^(-1/2x),x,0,infinity); 4 int(x/4*e^(-1/2x),x,0,infinity); 1 int(sqrt(2)*x^(1/2)*e^(-1/2x),x,0,infinity); 2*sqrt(pi) int(x^(3/2)*e^(-x),x,0,infinity); 3*sqrt(pi) ------------ 4 int(sqrt(pi)*x^(3/2)*e^(-x),x,0,infinity); 3*pi ------ 4 int(x*log(1+1/x),x,0,infinity); 1 int(x*log(1 + ---),x,0,infinity) x int(si(1/x),x,0,infinity); 1 int(si(---),x,0,infinity) x int(cos(1/x),x,0,infinity); 1 int(cos(---),x,0,infinity) x int(sin(x^2),x,0,infinity); sqrt(pi)*sqrt(2) ------------------ 4 int(sin(x^(3/2)),x,0,infinity); 2/3 5 sqrt(pi)*2 *gamma(---) 6 -------------------------- 2 3*gamma(---) 3 int(besselj(2,x),x,0,infinity); 1 int(besselj(2,y^(5/4)),y,0,infinity); 4/5 7 2*2 *gamma(---) 5 ------------------- 8 5*gamma(---) 5 int(x^(-1)*besselj(2,sqrt(x)),x,0,infinity); 1 int(bessely(2,x),x,0,infinity); int(bessely(2,x),x,0,infinity) int(x*besseli(2,x),x,0,infinity); int(x*besseli(2,x),x,0,infinity) int(besselk(0,x),x,0,infinity); pi ---- 2 int(x^2*besselk(2,x),x,0,infinity); 3*pi ------ 2 int(sinh(x),x,0,infinity); int(sinh(x),x,0,infinity) int(cosh(2*x),x,0,infinity); int(cosh(2*x),x,0,infinity) int(-3*ei(-x),x,0,infinity); 3 int(x*shi(x),x,0,infinity); int(x*shi(x),x,0,infinity) int(x*fresnel_c(x),x,0,infinity); int(x*fresnel_c(x),x,0,infinity) int(x^3*e^(-2*x),x,0,infinity); 3 --- 8 int(x^(-1)*sin(x/3),x,0,infinity); pi ---- 2 int(x^(-1/2)*sin(x),x,0,infinity); sqrt(pi)*sqrt(2) ------------------ 2 int(2*x^(-1/2)*cos(x),x,0,infinity); sqrt(pi)*sqrt(2) int(sin x + cos x,x,0,infinity); int(sin(x) + cos(x),x,0,infinity) int(ei(-x) + sin(x^2),x,0,infinity); sqrt(pi)*sqrt(2) - 4 ---------------------- 4 int(x^(-1)*(sin (-2*x) + sin(x^2)),x,0,infinity); - pi ------- 4 int(x^(-1)*(cos(x/2) - cos(x/3)),x,0,infinity); 3 - log(---) 2 int(x^(-1)*(cos x - cos(2*x)),x,0,infinity); log(2) int(x^(-1)*(cos(x) - cos(x)),x,0,infinity); 0 int(2,x,0,infinity); int(2,x,0,infinity) int(cos(x)*si(x),x,0,infinity); int(cos(x)*si(x),x,0,infinity) int(2*cos(x)*e^(-x),x,0,infinity); 1 int(x/2*cos(x)*e^(-x),x,0,infinity); 0 int(x^2/4*cos(x)*e^(-2*x),x,0,infinity); 1 ----- 125 int(1/(2*x)*sin(x)*e^(-3*x),x,0,infinity); 1 atan(---) 3 ----------- 2 int(3/x^2*sin(x)*e^(-x),x,0,infinity); 3 - x int(----*sin(x)*e ,x,0,infinity) 2 x int(cos(sqrt(x))*e^(-x),x,0,infinity); i 1/4 sqrt( - pi)*erf(---) + 2*e 2 ------------------------------- 1/4 2*e int(e^(-x)*besselj(2,x),x,0,infinity); - 2*sqrt(2) + 3 ------------------ sqrt(2) int(cos(x^2)*e^(-x),x,0,infinity); 1 1 1 1 1 (pi*( - 2*cos(---)*fresnel_s(---) + cos(---) + 2*fresnel_c(---)*sin(---) 4 4 4 4 4 1 - sin(---)))/(2*sqrt(pi)*sqrt(2)) 4 int(erf(x)*e^(-x),x,0,infinity); 1/4 1 e *( - erf(---) + 1) 2 int(besseli(2,x)*e^(-x),x,0,infinity); - 1 1 2*hypergeometric({------},{},1) + hypergeometric({---},{},1) - 2 2 2 int(e^(-x^2)*cos(x),x,0,infinity); sqrt(pi) ---------- 1/4 2*e int(x^(-1)*sin(x)*cos(x),x,0,infinity); pi ---- 4 int(x^(-1)*sin(x)*cos(2*x),x,0,infinity); 0 int(x^(-1)*sin(x)*cos(x/2),x,0,infinity); pi ---- 2 int(e^x,x,0,infinity); x int(e ,x,0,infinity) int(e^(-x^2 - x),x,0,infinity); 1/4 1 e *pi*( - erf(---) + 1) 2 --------------------------- 2*sqrt(pi) int(e^(-(x+x^2+1)),x,0,infinity); 1/4 1 e *pi*( - erf(---) + 1) 2 --------------------------- 2*sqrt(pi)*e int(e^(-(x+1/x)^2),x,0,infinity); sqrt(pi) ---------- 4 2*e int(e^(-(x+2))*sin(x),x,0,infinity); 1 ------ 2 2*e int(-3*x*e^(-1/2x),x,0,infinity); -12 int(x*e^(-1/2*x^2),x,0,infinity); 1 int(x^2*besselj(2,x),x,0,infinity); 2 int(x *besselj(2,x),x,0,infinity) int(x*besselk(1,x),x,0,infinity); pi ---- 2 int(-3*ei(-x),x,0,infinity); 3 int(x^3*e^(-2*x^2),x,0,infinity); 1 --- 8 int(sqrt(2)/2*x^(-3/2)*sin x,x,0,infinity); sqrt(pi) int(x^(-1)*(sin(-2*x) + sin(x^2)),x,0,infinity); - pi ------- 4 int(x^(-1)*(cos(3*x) - cos(x/2)),x,0,infinity); - log(6) int(x^(-1)*(sin x - sin(2*x)),x,0,infinity); 0 int(1/x*sin(x)*e^(-3*x),x,0,infinity); 1 atan(---) 3 int(sin(x)*e^(-x),x,0,infinity); 1 --- 2 int(x^(-1)*sin(x)*cos(x),x,0,infinity); pi ---- 4 int(e^(1-x)*e^(2-x^2),x,0,infinity); 1/4 3 1 e *e *pi*( - erf(---) + 1) 2 ------------------------------ 2*sqrt(pi) int(e^(-1/2x),x,0,y); y/2 2*(e - 1) -------------- y/2 e int(si(x),x,0,y); cos(y) + si(y)*y - 1 int(besselj(2,x^(1/4)),x,0,y); 1/4 4*besselj(3,y )*y --------------------- 1/4 y int(x*besseli(2,x),x,0,y); besseli(1,y)*y - 2*besseli(0,y) + 2 int(x^(3/2)*e^(-x),x,0,y); y 3*sqrt(pi)*e *erf(sqrt(y)) - 4*sqrt(y)*y - 6*sqrt(y) ------------------------------------------------------ y 4*e int(sinh(x),x,0,y); 2*y y e - 2*e + 1 ----------------- y 2*e int(cosh(2*x),x,0,y); 4*y e - 1 ---------- 2*y 4*e int(x*shi(x),x,0,y); 2*y 2*y y 2 - e *y + e + 2*e *shi(y)*y - y - 1 ------------------------------------------- y 4*e int(x^2*e^(-x^2),x,0,y); 2 y sqrt(pi)*e *erf(y) - 2*y --------------------------- 2 y 4*e int(x^(-1)/2*sin(x),x,0,y); si(y) ------- 2 int(sin x + cos x,x,0,y); - cos(y) + sin(y) + 1 int(sin x + sin(-2*x),x,0,y); cos(2*y) - 2*cos(y) + 1 ------------------------- 2 int(sin(n*x),x,0,y); - cos(n*y) + 1 ----------------- n int(heaviside(x-1),x,0,y); heaviside(y - 1)*(y - 1) % Tests of transformations defined in defint package. laplace_transform(1,x); 1 --- s laplace_transform(x,x); 1 ---- 2 s laplace_transform(x^a/factorial(a),x); 1 ------ a s *s laplace_transform(x,e^(-a*x),x); 1 ----------------- 2 2 a + 2*a*s + s laplace_transform(x^k,e^(-a*x),x); gamma(k + 1) ------------------------- k k (a + s) *a + (a + s) *s laplace_transform(cosh(a*x),x); - s --------- 2 2 a - s laplace_transform(1/(2*a^3),sinh(a*x)-sin(a*x),x); - 1 --------- 4 4 a - s laplace_transform(1/(a^2),1-cos(a*x),x); 1 ----------- 2 3 a *s + s laplace_transform(1/(b^2-a^2),cos(a*x)-cos(b*x),x); s ---------------------------- 2 2 2 2 2 2 4 a *b + a *s + b *s + s laplace_transform(besselj(0,2*sqrt(k*x)),x); 1 -------- k/s e *s laplace_transform(Heaviside(x-1),x); 1 ------ s e *s laplace_transform(1/x,sin(k*x),x); k atan(---) s laplace_transform(1/(k*sqrt(pi)),e^(-x^2/(4*k^2)),x); 2 2 2 2 k *s k *s - e *erf(k*s) + e laplace_transform(1/k,e^(-k^2/(4*x)),x); besselk(1,sqrt(s)*k) ---------------------- sqrt(s) laplace_transform(2/(sqrt(pi*x)),besselk(0,2*sqrt(2*k*x)),x); k/s k e *besselk(0,---) s --------------------- sqrt(s) hankel_transform(x,x); n + 4 gamma(-------) 2 ------------------- n - 2 2 gamma(-------)*s 2 Y_transform(x,x); - n + 4 n + 4 gamma(----------)*gamma(-------) 2 2 ------------------------------------- - n + 3 n - 1 2 gamma(----------)*gamma(-------)*s 2 2 K_transform(x,x); - n + 4 n + 4 gamma(----------)*gamma(-------) 2 2 ---------------------------------- 2 2*s struveh_transform(x,x); - n - 3 n + 5 gamma(----------)*gamma(-------) 2 2 ------------------------------------- - n - 2 n - 2 2 gamma(----------)*gamma(-------)*s 2 2 fourier_sin(e^(-x),x); s -------- 2 s + 1 fourier_sin(sqrt(x),e^(-1/2*x),x); 3*atan(2*s) 2*sin(-------------)*pi 2 -------------------------------- 2 3/4 sqrt(pi)*(4*s + 1) *sqrt(2) fourier_sin(1/x,e^(-a*x),x); s atan(---) a fourier_sin(x^k,x); k/2 - k k 4 *gamma(------)*gamma(---)*k 2 2 --------------------------------- k k 4*s *2 *gamma( - k)*s fourier_sin(1/(b-a),(e^(-a*x)-e^(-b*x)),x); a*s + b*s ---------------------------- 2 2 2 2 2 2 4 a *b + a *s + b *s + s fourier_sin(besselj(0,a*x),x); 2 2 - a + s heaviside(------------) 2 a ------------------------- 2 2 sqrt( - a + s ) fourier_sin(1/sqrt(pi*x),cos(2*sqrt(k*x)),x); k k sqrt(s)*sqrt(2)*cos(---) - sqrt(s)*sqrt(2)*sin(---) s s ----------------------------------------------------- 2*s fourier_sin(1/(k*sqrt(pi)),e^(-x^2/(4*k^2)),x); sqrt( - pi)*erf(i*k*s) ------------------------ 2 2 k *s sqrt(pi)*e fourier_cos(e^(-1/2x),x); 2 ---------- 2 4*s + 1 fourier_cos(x,e^(-x),x); 2 - s + 1 --------------- 4 2 s + 2*s + 1 fourier_cos(x,e^(-1/2*x^2),x); 2 i*s s /2 sqrt( - pi)*erf(---------)*s + e *sqrt(2) sqrt(2) ---------------------------------------------- 2 s /2 e *sqrt(2) fourier_cos(2*x^2,e^(-1/2x),x); 2 - 384*s + 32 --------------------------- 6 4 2 64*s + 48*s + 12*s + 1 fourier_cos(x,e^(-a*x),x); 2 2 a - s ------------------- 4 2 2 4 a + 2*a *s + s fourier_cos(x^n,e^(-a*x),x); s s cos(atan(---)*n + atan(---))*gamma(n + 1) a a ------------------------------------------- 2 2 (n + 1)/2 (a + s ) fourier_cos(1/x,sin(k*x),x); 2 2 sign(k - s )*pi + pi ----------------------- 4 fourier_cos(1/sqrt(pi*x),cos(2*sqrt(k*x)),x); k k sqrt(s)*sqrt(2)*cos(---) + sqrt(s)*sqrt(2)*sin(---) s s ----------------------------------------------------- 2*s fourier_cos(1/(k*sqrt(pi)),e^(-x^2/(4*k^2)),x); 1 -------- 2 2 k *s e fourier_cos(1/(pi*x),sin(2*k*sqrt(x)),x); 2 2 k k intfc(----) + intfs(----) s s fourier_cos(1/(sqrt(pi*x)),e^(-2*k*sqrt(x)),x); 2 2 2 k k k ( - 2*sqrt(s)*cos(----)*fresnel_s(----) + sqrt(s)*cos(----) s s s 2 2 2 k k k + 2*sqrt(s)*fresnel_c(----)*sin(----) - sqrt(s)*sin(----))/(sqrt(2)*s) s s s laplace_transform(x^n/factorial(n)*e^(-a*x),x); 1 ------------------------- n n (a + s) *a + (a + s) *s laplace_transform(1/(2*a^2)*(cosh(a*x)-cos(a*x)),x); - s --------- 4 4 a - s laplace_transform(k*a^k/x*besselj(k,a*x),x); 2*k a ---------------------- 2 2 k (sqrt(a + s ) + s) fourier_sin(1/x*e^(-3*x),x); s atan(---) 3 fourier_sin(1/(pi*x)*sin(2*k*sqrt(x)),x); 2 2 k k intfc(----) - intfs(----) s s fourier_cos(x^n*e^(-a*x),x); s s cos(atan(---)*n + atan(---))*gamma(n + 1) a a ------------------------------------------- 2 2 (n + 1)/2 (a + s ) fourier_cos(1/(k*sqrt(pi))*e^(-x^2/(4*k^2)),x); 1 -------- 2 2 k *s e end; (TIME: defint 163620 182910)