1 / | | 1 | ----------- dx | ________ | / 2 | \/ x + 1 | / 0
Integral(1/(sqrt(x^2 + 1)), (x, 0, 1))
TrigSubstitutionRule(theta=_theta, func=tan(_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=True, context=1/(sqrt(x**2 + 1)), symbol=x)
Add the constant of integration:
The answer is:
/ | / ________\ | 1 | / 2 | | ----------- dx = C + log\x + \/ 1 + x / | ________ | / 2 | \/ x + 1 | /
/ ___\ log\1 + \/ 2 /
=
/ ___\ log\1 + \/ 2 /
log(1 + sqrt(2))
Use the examples entering the upper and lower limits of integration.