1 / | | 1 | ------ dx | 2 | x - 3 | / 0
Integral(1/(x^2 - 3), (x, 0, 1))
PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=-3, context=1/(x**2 - 3), symbol=x), False), (ArccothRule(a=1, b=1, c=-3, context=1/(x**2 - 3), symbol=x), x**2 > 3), (ArctanhRule(a=1, b=1, c=-3, context=1/(x**2 - 3), symbol=x), x**2 < 3)], context=1/(x**2 - 3), symbol=x)
Add the constant of integration:
The answer is:
// / ___\ \ || ___ |x*\/ 3 | | ||-\/ 3 *acoth|-------| | / || \ 3 / 2 | | ||---------------------- for x > 3| | 1 || 3 | | ------ dx = C + |< | | 2 || / ___\ | | x - 3 || ___ |x*\/ 3 | | | ||-\/ 3 *atanh|-------| | / || \ 3 / 2 | ||---------------------- for x < 3| \\ 3 /
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\ \/ 3 *\pi*I + log\\/ 3 // \/ 3 *log\1 + \/ 3 / \/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\\/ 3 / - ------------------------- - -------------------- + ------------------------------ + ---------------- 6 6 6 6
=
___ / / ___\\ ___ / ___\ ___ / / ___\\ ___ / ___\ \/ 3 *\pi*I + log\\/ 3 // \/ 3 *log\1 + \/ 3 / \/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\\/ 3 / - ------------------------- - -------------------- + ------------------------------ + ---------------- 6 6 6 6
-sqrt(3)*(pi*i + log(sqrt(3)))/6 - sqrt(3)*log(1 + sqrt(3))/6 + sqrt(3)*(pi*i + log(-1 + sqrt(3)))/6 + sqrt(3)*log(sqrt(3))/6
Use the examples entering the upper and lower limits of integration.