1 / | | 1 | 1*-------------- dx | ___________ | / 2 | \/ 4 - 25*x | / 0
TrigSubstitutionRule(theta=_theta, func=2*sin(_theta)/5, rewritten=1/5, substep=ConstantRule(constant=1/5, context=1/5, symbol=_theta), restriction=(x > -2/5) & (x < 2/5), context=1/sqrt(4 - 25*x**2), symbol=x)
Now simplify:
Add the constant of integration:
The answer is:
/ | // /5*x\ \ | 1 ||asin|---| | | 1*-------------- dx = C + |< \ 2 / | | ___________ ||--------- for And(x > -2/5, x < 2/5)| | / 2 \\ 5 / | \/ 4 - 25*x | /
asin(5/2) --------- 5
=
asin(5/2) --------- 5
(0.286954509007177 - 0.320835134585762j)
(0.286954509007177 - 0.320835134585762j)
Use the examples entering the upper and lower limits of integration.