1 / | | x + 3 | ------------ dx | 2 | x - 2*x - 5 | / 0
Integral((x + 3)/(x^2 - 2*x - 5), (x, 0, 1))
// / ___ \ \ || ___ |\/ 6 *(-1 + x)| | ||-\/ 6 *acoth|--------------| | / || \ 6 / 2 | | / 2 \ ||----------------------------- for (-1 + x) > 6| | x + 3 log\-5 + x - 2*x/ || 6 | | ------------ dx = C + ------------------ + 4*|< | | 2 2 || / ___ \ | | x - 2*x - 5 || ___ |\/ 6 *(-1 + x)| | | ||-\/ 6 *atanh|--------------| | / || \ 6 / 2 | ||----------------------------- for (-1 + x) < 6| \\ 6 /
/ ___\ / ___\ / ___\ / ___\ |1 \/ 6 | / ___\ |1 \/ 6 | / / ___\\ |1 \/ 6 | / ___\ |1 \/ 6 | / / ___\\ |- - -----|*log\\/ 6 / + |- + -----|*\pi*I + log\\/ 6 // - |- - -----|*log\-1 + \/ 6 / - |- + -----|*\pi*I + log\1 + \/ 6 // \2 3 / \2 3 / \2 3 / \2 3 /
=
/ ___\ / ___\ / ___\ / ___\ |1 \/ 6 | / ___\ |1 \/ 6 | / / ___\\ |1 \/ 6 | / ___\ |1 \/ 6 | / / ___\\ |- - -----|*log\\/ 6 / + |- + -----|*\pi*I + log\\/ 6 // - |- - -----|*log\-1 + \/ 6 / - |- + -----|*\pi*I + log\1 + \/ 6 // \2 3 / \2 3 / \2 3 / \2 3 /
(1/2 - sqrt(6)/3)*log(sqrt(6)) + (1/2 + sqrt(6)/3)*(pi*i + log(sqrt(6))) - (1/2 - sqrt(6)/3)*log(-1 + sqrt(6)) - (1/2 + sqrt(6)/3)*(pi*i + log(1 + sqrt(6)))
Use the examples entering the upper and lower limits of integration.