# What is the substitution for the integral?

the formula needs to be used from left to right. The substitution x = sin(u), dx = cos(u) du is useful because 1 − sin 2 ⁡ u = cos ⁡ ( u ) {\displaystyle {\sqrt {1-\sin ^{2}u}}=\cos(u)} : The resulting integral can be computed using integration by parts or a double angle formula followed by one more substitution.