# Evaluate the definite integral. {eq}\displaystyle \int tan^2\ x\ sec^4\ x {/eq}

## Question:

Evaluate the definite integral.

{eq}\displaystyle \int tan^2\ x\ sec^4\ x {/eq}

## Indefinite Integral in Calculus:

In this problem, we need to find out the indefinite integral of the given trigonometric function. To solve this problem, we'll use substitution to get the standard form of the integrand.

In this problem, we'll also use the trigonometric identity including tangent and secant function.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer!

We are given:

{eq}\displaystyle \int \tan ^{2}x\sec ^{4}x \ dx {/eq}

{eq}=\displaystyle \int \sec ^{2}x \sec ^{2}x \tan ^{2}x \ dx {/eq}

Now...

See full answer below.