## [Maxima-commits] CVS: maxima/tests rtestint.mac,1.15,1.16

 [Maxima-commits] CVS: maxima/tests rtestint.mac,1.15,1.16 From: Raymond Toy - 2006-03-28 16:23:37 ```Update of /cvsroot/maxima/maxima/tests In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv28905/tests Modified Files: rtestint.mac Log Message: o Fix typo in test for Bug 1451351. o Add tests from p. 94, 102, and 103 from Wang's thesis. (Needs verification.) Index: rtestint.mac =================================================================== RCS file: /cvsroot/maxima/maxima/tests/rtestint.mac,v retrieving revision 1.15 retrieving revision 1.16 diff -u -d -r1.15 -r1.16 --- rtestint.mac 28 Mar 2006 05:29:11 -0000 1.15 +++ rtestint.mac 28 Mar 2006 16:23:32 -0000 1.16 @@ -540,9 +540,22 @@ * This is the same integral as above, using the substitution * y=log(x). See also Bug 1451351. */ -integrate(x*exp((kj+1)*x)/(exp(3)+3),x,minf,inf); +integrate(x*exp((kj+1)*x)/(exp(x)+3),x,minf,inf); 3^kj*(psi[0](kj+1)-psi[0](-kj))*beta(kj+1,-kj)+log(3)*3^kj*beta(kj+1,-kj); +/* p. 94 + * + * The default gcd gets a "quotient is not exact" error. spmod works better. + */ +gcd:spmod; +spmod; + +integrate((atan(x^(1/3)) + atan(x^(-1/3)))*log(x)/(x^2+1),x,0,inf); +0; + +gcd:subres; +subres; + /* p. 95 */ /* * Wang gives %pi/sin(5*%pi/7) @@ -609,6 +622,31 @@ integrate(exp(-x^2),x,0,inf); sqrt(%pi)/2; +/* p. 102 */ +(assume(s > 0), 0); +0; +integrate(1/sqrt(t)/exp(s*t),t,0,inf); +sqrt(%pi)/sqrt(s); + +integrate(sin(s*x)/exp(x),x,0,inf); +s/(s^2+1); + +/* p. 103 */ +/* + * There's a typo in Wang's thesis. He has the integrand as + * exp(-s*t)*x^(1/3)*log(x). I changed the x's to t's. + * + * Also, Wang says the answer is + * + * -gamma(1/3)*(log(s)-psi(4/3))/(6*s^(4/3)) + * + * Assuming psi(4/3) is maxima's digamma function, psi[0](4/3), this + * result is 1/2 of the result maxima produces. + */ +integrate(exp(-s*t)*t^(1/3)*log(t),t,0,inf); +gamma(1/3)*(-3*log(3)/2-%pi/(2*sqrt(3))-%gamma+3)/(3*s^(4/3)) + -gamma(1/3)*log(s)/(3*s^(4/3)); + /* p. 106 */ /* Verified via indefinite integral */ integrate(1/(x^2-3),x,0,1); ```

 [Maxima-commits] CVS: maxima/tests rtestint.mac,1.15,1.16 From: Raymond Toy - 2006-03-28 16:23:37 ```Update of /cvsroot/maxima/maxima/tests In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv28905/tests Modified Files: rtestint.mac Log Message: o Fix typo in test for Bug 1451351. o Add tests from p. 94, 102, and 103 from Wang's thesis. (Needs verification.) Index: rtestint.mac =================================================================== RCS file: /cvsroot/maxima/maxima/tests/rtestint.mac,v retrieving revision 1.15 retrieving revision 1.16 diff -u -d -r1.15 -r1.16 --- rtestint.mac 28 Mar 2006 05:29:11 -0000 1.15 +++ rtestint.mac 28 Mar 2006 16:23:32 -0000 1.16 @@ -540,9 +540,22 @@ * This is the same integral as above, using the substitution * y=log(x). See also Bug 1451351. */ -integrate(x*exp((kj+1)*x)/(exp(3)+3),x,minf,inf); +integrate(x*exp((kj+1)*x)/(exp(x)+3),x,minf,inf); 3^kj*(psi[0](kj+1)-psi[0](-kj))*beta(kj+1,-kj)+log(3)*3^kj*beta(kj+1,-kj); +/* p. 94 + * + * The default gcd gets a "quotient is not exact" error. spmod works better. + */ +gcd:spmod; +spmod; + +integrate((atan(x^(1/3)) + atan(x^(-1/3)))*log(x)/(x^2+1),x,0,inf); +0; + +gcd:subres; +subres; + /* p. 95 */ /* * Wang gives %pi/sin(5*%pi/7) @@ -609,6 +622,31 @@ integrate(exp(-x^2),x,0,inf); sqrt(%pi)/2; +/* p. 102 */ +(assume(s > 0), 0); +0; +integrate(1/sqrt(t)/exp(s*t),t,0,inf); +sqrt(%pi)/sqrt(s); + +integrate(sin(s*x)/exp(x),x,0,inf); +s/(s^2+1); + +/* p. 103 */ +/* + * There's a typo in Wang's thesis. He has the integrand as + * exp(-s*t)*x^(1/3)*log(x). I changed the x's to t's. + * + * Also, Wang says the answer is + * + * -gamma(1/3)*(log(s)-psi(4/3))/(6*s^(4/3)) + * + * Assuming psi(4/3) is maxima's digamma function, psi[0](4/3), this + * result is 1/2 of the result maxima produces. + */ +integrate(exp(-s*t)*t^(1/3)*log(t),t,0,inf); +gamma(1/3)*(-3*log(3)/2-%pi/(2*sqrt(3))-%gamma+3)/(3*s^(4/3)) + -gamma(1/3)*log(s)/(3*s^(4/3)); + /* p. 106 */ /* Verified via indefinite integral */ integrate(1/(x^2-3),x,0,1); ```