Learn how to solve problems step by step online. Integrate int(x^3(1+81x^2)^(1/2))dx. First, factor the terms inside the radical by 81 for an easier handling. Taking the constant out of the radical. We can solve the integral \int9x^3\sqrt{\frac{1}{81}+x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above.

Integrate int(x^3(1+81x^2)^(1/2))dx