# Evaluate the integral using the indicated trigonometric substitution. integral {x^3} / {(x^2 +...

## Question:

Evaluate the integral using the indicated trigonometric substitution.

{eq}\displaystyle \int \frac {x^3} {(x^2 + 25)^{\frac 1 2}}\ dx,\ x = 5 \tan \theta {/eq}.

## Integrals:

The given indefinite integral is complex to solve. As we cannot solve the given integral directly, therefore we will simplify the function by applying the substitution method. The substitution for the variable is already given to us.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer!

{eq}\begin{align*} & \int \frac {x^3} {(x^2 + 25)^{\frac 1 2}} \ dx \end{align*} {/eq}

Put,

{eq}\begin{align*} & x = 5 \tan \theta...

See full answer below.