Learn how to solve problems step by step online. Find the integral int((y^3)/((a^2-y^2)^(3/2)))dy. We can solve the integral \int\frac{y^3}{\sqrt{\left(a^2-y^2\right)^{3}}}dy by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dy, we need to find the derivative of y. We need to calculate dy, we can do that by deriving the equation above. Substituting in the original integral, we get. Factor the polynomial a^2-a^2\sin\left(\theta \right)^2 by it's greatest common factor (GCF): a^2.

Find the integral int((y^3)/((a^2-y^2)^(3/2)))dy