Integrate $\int x^3\sqrt{x^2+16}dx$

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

Learn how to solve problems step by step online. Integrate int(x^3(x^2+16)^(1/2))dx. We can solve the integral \int x^3\sqrt{x^2+16}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. Apply the formula: \int cxdx=c\int xdx, where c=1024 and x=\tan\left(\theta \right)^3\sec\left(\theta \right)^{3}.