1 / | | 1 | ----------- dx | ________ | / 2 | \/ x - 1 | / 0
Integral(1/(sqrt(x^2 - 1)), (x, 0, 1))
TrigSubstitutionRule(theta=_theta, func=sec(_theta), rewritten=sec(_theta), substep=RewriteRule(rewritten=(tan(_theta)*sec(_theta) + sec(_theta)**2)/(tan(_theta) + sec(_theta)), substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=tan(_theta) + sec(_theta), constant=1, substep=ReciprocalRule(func=_u, context=1/_u, symbol=_u), context=(tan(_theta)*sec(_theta) + sec(_theta)**2)/(tan(_theta) + sec(_theta)), symbol=_theta)], context=(tan(_theta)*sec(_theta) + sec(_theta)**2)/(tan(_theta) + sec(_theta)), symbol=_theta), context=sec(_theta), symbol=_theta), restriction=(x > -1) & (x < 1), context=1/(sqrt(x**2 - 1)), symbol=x)
Add the constant of integration:
The answer is:
/ | | 1 // / _________\ \ | ----------- dx = C + |< | / 2 | | | ________ \\log\x + \/ -1 + x / for And(x > -1, x < 1)/ | / 2 | \/ x - 1 | /
-pi*I ------ 2
=
-pi*I ------ 2
-pi*i/2
Use the examples entering the upper and lower limits of integration.