Artifact baf18d31614b12a94eb1a97fbe9c0db0b24ee2ce920b05d6e32a43af926c4a12:
- Executable file
r36/XMPL/DEFINT.TST
— 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: 4939) [annotate] [blame] [check-ins using] [more...]
% Test cases for definite integration. int(x/(x+2),x,2,6); int(sin x,x,0,pi/2); int(log(x),x,1,5); int((1+x**2/p**2)**(1/2),x,0,p); int(x**9+y+y**x+x,x,0,2); % Collected by Kerry Gaskell, ZIB, 1993/94. int(x^2*log(1+x),x,0,infinity); int(x*e^(-1/2x),x,0,infinity); int(x/4*e^(-1/2x),x,0,infinity); int(sqrt(2)*x^(1/2)*e^(-1/2x),x,0,infinity); int(x^(3/2)*e^(-x),x,0,infinity); int(sqrt(pi)*x^(3/2)*e^(-x),x,0,infinity); int(x*log(1+1/x),x,0,infinity); int(si(1/x),x,0,infinity); int(cos(1/x),x,0,infinity); int(sin(x^2),x,0,infinity); int(sin(x^(3/2)),x,0,infinity); int(besselj(2,x),x,0,infinity); int(besselj(2,y^(5/4)),y,0,infinity); int(x^(-1)*besselj(2,sqrt(x)),x,0,infinity); int(bessely(2,x),x,0,infinity); int(x*besseli(2,x),x,0,infinity); int(besselk(0,x),x,0,infinity); int(x^2*besselk(2,x),x,0,infinity); int(sinh(x),x,0,infinity); int(cosh(2*x),x,0,infinity); int(-3*ei(-x),x,0,infinity); int(x*shi(x),x,0,infinity); int(x*fresnel_c(x),x,0,infinity); int(x^3*e^(-2*x),x,0,infinity); int(x^(-1)*sin(x/3),x,0,infinity); int(x^(-1/2)*sin(x),x,0,infinity); int(2*x^(-1/2)*cos(x),x,0,infinity); int(sin x + cos x,x,0,infinity); int(ei(-x) + sin(x^2),x,0,infinity); int(x^(-1)*(sin (-2*x) + sin(x^2)),x,0,infinity); int(x^(-1)*(cos(x/2) - cos(x/3)),x,0,infinity); int(x^(-1)*(cos x - cos(2*x)),x,0,infinity); int(x^(-1)*(cos(x) - cos(x)),x,0,infinity); int(2,x,0,infinity); int(cos(x)*si(x),x,0,infinity); int(2*cos(x)*e^(-x),x,0,infinity); int(x/2*cos(x)*e^(-x),x,0,infinity); int(x^2/4*cos(x)*e^(-2*x),x,0,infinity); int(1/(2*x)*sin(x)*e^(-3*x),x,0,infinity); int(3/x^2*sin(x)*e^(-x),x,0,infinity); int(cos(sqrt(x))*e^(-x),x,0,infinity); int(e^(-x)*besselj(2,x),x,0,infinity); int(cos(x^2)*e^(-x),x,0,infinity); int(erf(x)*e^(-x),x,0,infinity); int(besseli(2,x)*e^(-x),x,0,infinity); int(e^(-x^2)*cos(x),x,0,infinity); int(x^(-1)*sin(x)*cos(x),x,0,infinity); int(x^(-1)*sin(x)*cos(2*x),x,0,infinity); int(x^(-1)*sin(x)*cos(x/2),x,0,infinity); int(e^x,x,0,infinity); int(e^(-x^2 - x),x,0,infinity); int(e^(-(x+x^2+1)),x,0,infinity); int(e^(-(x+1/x)^2),x,0,infinity); int(e^(-(x+2))*sin(x),x,0,infinity); int(-3*x*e^(-1/2x),x,0,infinity); int(x*e^(-1/2*x^2),x,0,infinity); int(x^2*besselj(2,x),x,0,infinity); int(x*besselk(1,x),x,0,infinity); int(-3*ei(-x),x,0,infinity); int(x^3*e^(-2*x^2),x,0,infinity); int(sqrt(2)/2*x^(-3/2)*sin x,x,0,infinity); int(x^(-1)*(sin(-2*x) + sin(x^2)),x,0,infinity); int(x^(-1)*(cos(3*x) - cos(x/2)),x,0,infinity); int(x^(-1)*(sin x - sin(2*x)),x,0,infinity); int(1/x*sin(x)*e^(-3*x),x,0,infinity); int(sin(x)*e^(-x),x,0,infinity); int(x^(-1)*sin(x)*cos(x),x,0,infinity); int(e^(1-x)*e^(2-x^2),x,0,infinity); int(e^(-1/2x),x,0,y); int(si(x),x,0,y); int(besselj(2,x^(1/4)),x,0,y); int(x*besseli(2,x),x,0,y); int(x^(3/2)*e^(-x),x,0,y); int(sinh(x),x,0,y); int(cosh(2*x),x,0,y); int(x*shi(x),x,0,y); int(x^2*e^(-x^2),x,0,y); int(x^(-1)/2*sin(x),x,0,y); int(sin x + cos x,x,0,y); int(sin x + sin(-2*x),x,0,y); int(sin(n*x),x,0,y); int(heaviside(x-1),x,0,y); % Tests of transformations defined in defint package. laplace_transform(1,x); laplace_transform(x,x); laplace_transform(x^a/factorial(a),x); laplace_transform(x,e^(-a*x),x); laplace_transform(x^k,e^(-a*x),x); laplace_transform(cosh(a*x),x); laplace_transform(1/(2*a^3),sinh(a*x)-sin(a*x),x); laplace_transform(1/(a^2),1-cos(a*x),x); laplace_transform(1/(b^2-a^2),cos(a*x)-cos(b*x),x); laplace_transform(besselj(0,2*sqrt(k*x)),x); laplace_transform(Heaviside(x-1),x); laplace_transform(1/x,sin(k*x),x); laplace_transform(1/(k*sqrt(pi)),e^(-x^2/(4*k^2)),x); laplace_transform(1/k,e^(-k^2/(4*x)),x); laplace_transform(2/(sqrt(pi*x)),besselk(0,2*sqrt(2*k*x)),x); hankel_transform(x,x); Y_transform(x,x); K_transform(x,x); struveh_transform(x,x); fourier_sin(e^(-x),x); fourier_sin(sqrt(x),e^(-1/2*x),x); fourier_sin(1/x,e^(-a*x),x); fourier_sin(x^k,x); fourier_sin(1/(b-a),(e^(-a*x)-e^(-b*x)),x); fourier_sin(besselj(0,a*x),x); fourier_sin(1/sqrt(pi*x),cos(2*sqrt(k*x)),x); fourier_sin(1/(k*sqrt(pi)),e^(-x^2/(4*k^2)),x); fourier_cos(e^(-1/2x),x); fourier_cos(x,e^(-x),x); fourier_cos(x,e^(-1/2*x^2),x); fourier_cos(2*x^2,e^(-1/2x),x); fourier_cos(x,e^(-a*x),x); fourier_cos(x^n,e^(-a*x),x); fourier_cos(1/x,sin(k*x),x); fourier_cos(1/sqrt(pi*x),cos(2*sqrt(k*x)),x); fourier_cos(1/(k*sqrt(pi)),e^(-x^2/(4*k^2)),x); fourier_cos(1/(pi*x),sin(2*k*sqrt(x)),x); fourier_cos(1/(sqrt(pi*x)),e^(-2*k*sqrt(x)),x); laplace_transform(x^n/factorial(n)*e^(-a*x),x); laplace_transform(1/(2*a^2)*(cosh(a*x)-cos(a*x)),x); laplace_transform(k*a^k/x*besselj(k,a*x),x); fourier_sin(1/x*e^(-3*x),x); fourier_sin(1/(pi*x)*sin(2*k*sqrt(x)),x); fourier_cos(x^n*e^(-a*x),x); fourier_cos(1/(k*sqrt(pi))*e^(-x^2/(4*k^2)),x); end;