# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\frac{x^3}{\sqrt{16-x^2}}dx$

Learn how to solve integrals of rational functions problems step by step online.

$x=4\sin\left(\theta \right)$

Learn how to solve integrals of rational functions problems step by step online. Integral of (x^3)/((16-x^2)^0.5) with respect to x. We can solve the integral \int\frac{x^3}{\sqrt{16-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. Substituting in the original integral, we get. Factor by the greatest common divisor 16.

$-16\sqrt{16-x^2}+\frac{1}{3}\sqrt{\left(16-x^2\right)^{3}}+C_0$

### Problem Analysis

$\int\frac{x^3}{\sqrt{16-x^2}}dx$

### Main topic:

Integrals of Rational Functions

~ 0.21 seconds