# Evaluate the integral: integral of 2sec^4 x dx.

## Question:

Evaluate the integral: {eq}\int 2 \sec^4 x \, \mathrm{d}x {/eq}.

## Indefinite Integral in Calculus:

The process of finding a function when it's derivetive is given is called anti-differentiation or integration. The symbol {eq}\int {/eq} represents integration, and {eq}dx {/eq} is a differential of the variable {eq}x {/eq} , which is a very small width of {eq}x {/eq}.

To solve this problem, we'll use the u-substitution.

We are given:

{eq}\displaystyle \int 2 \sec^4 x \, \mathrm{d}x {/eq}

Take the constant out:

{eq}= \displaystyle 2 \int \sec^4 x \,...

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