pi / | | _____ /x\ | \/ 2*x *sin|-| dx | \4/ | / -pi
Integral(sqrt(2*x)*sin(x/4), (x, -pi, pi))
___ ___ \/ 2 *\/ x / / | | | ____ / 2\ | _____ /x\ | / 2 |u | | \/ 2*x *sin|-| dx = C + | \/ u *u*sin|--| du | \4/ | \8 / | | / /
/ / ___\ \ / / ___\ \ | ___ ____ |\/ 2 | | | ___ ____ |\/ 2 | | | ___ ____ 5*\/ 2 *\/ pi *C|-----|*Gamma(5/4)| | ___ ____ 5*I*\/ 2 *\/ pi *C|-----|*Gamma(5/4)| ___ | 5*\/ 2 *\/ pi *Gamma(5/4) \ 2 / | ___ | 5*I*\/ 2 *\/ pi *Gamma(5/4) \ 2 / | \/ 2 *|- ------------------------- + ----------------------------------| - \/ 2 *|- --------------------------- + ------------------------------------| \ 2*Gamma(9/4) Gamma(9/4) / \ 2*Gamma(9/4) Gamma(9/4) /
=
/ / ___\ \ / / ___\ \ | ___ ____ |\/ 2 | | | ___ ____ |\/ 2 | | | ___ ____ 5*\/ 2 *\/ pi *C|-----|*Gamma(5/4)| | ___ ____ 5*I*\/ 2 *\/ pi *C|-----|*Gamma(5/4)| ___ | 5*\/ 2 *\/ pi *Gamma(5/4) \ 2 / | ___ | 5*I*\/ 2 *\/ pi *Gamma(5/4) \ 2 / | \/ 2 *|- ------------------------- + ----------------------------------| - \/ 2 *|- --------------------------- + ------------------------------------| \ 2*Gamma(9/4) Gamma(9/4) / \ 2*Gamma(9/4) Gamma(9/4) /
sqrt(2)*(-5*sqrt(2)*sqrt(pi)*gamma(5/4)/(2*gamma(9/4)) + 5*sqrt(2)*sqrt(pi)*fresnelc(sqrt(2)/2)*gamma(5/4)/gamma(9/4)) - sqrt(2)*(-5*i*sqrt(2)*sqrt(pi)*gamma(5/4)/(2*gamma(9/4)) + 5*i*sqrt(2)*sqrt(pi)*fresnelc(sqrt(2)/2)*gamma(5/4)/gamma(9/4))
Use the examples entering the upper and lower limits of integration.