1 / | | 1 | ------ dy | 2 | y - 2 | / 0
Integral(1/(y^2 - 2), (y, 0, 1))
PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=-2, context=1/(y**2 - 2), symbol=y), False), (ArccothRule(a=1, b=1, c=-2, context=1/(y**2 - 2), symbol=y), y**2 > 2), (ArctanhRule(a=1, b=1, c=-2, context=1/(y**2 - 2), symbol=y), y**2 < 2)], context=1/(y**2 - 2), symbol=y)
Add the constant of integration:
The answer is:
// / ___\ \ || ___ |y*\/ 2 | | ||-\/ 2 *acoth|-------| | / || \ 2 / 2 | | ||---------------------- for y > 2| | 1 || 2 | | ------ dy = C + |< | | 2 || / ___\ | | y - 2 || ___ |y*\/ 2 | | | ||-\/ 2 *atanh|-------| | / || \ 2 / 2 | ||---------------------- for y < 2| \\ 2 /
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\ \/ 2 *\pi*I + log\\/ 2 // \/ 2 *log\1 + \/ 2 / \/ 2 *\pi*I + log\-1 + \/ 2 // \/ 2 *log\\/ 2 / - ------------------------- - -------------------- + ------------------------------ + ---------------- 4 4 4 4
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\ \/ 2 *\pi*I + log\\/ 2 // \/ 2 *log\1 + \/ 2 / \/ 2 *\pi*I + log\-1 + \/ 2 // \/ 2 *log\\/ 2 / - ------------------------- - -------------------- + ------------------------------ + ---------------- 4 4 4 4
-sqrt(2)*(pi*i + log(sqrt(2)))/4 - sqrt(2)*log(1 + sqrt(2))/4 + sqrt(2)*(pi*i + log(-1 + sqrt(2)))/4 + sqrt(2)*log(sqrt(2))/4
Use the examples entering the upper and lower limits of integration.