# Evaluate the integral: {eq}\displaystyle \int \frac{sec^2\ x}{tan^2\ x + 2\ tan\ x + 2}\ dx {/eq}

## Question:

Evaluate the integral:

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

## Variable Substitution:

Indefinite integrals have a wide variety of techniques available for solving. One of these techniques is variable substitution. Variable substitution assigns a single variable for an entire expression of the original integrand, thus greatly simplifying the integration process. To use the technique effectively, the derivative of the new variable (in terms of the expression) must also be found inside the original integrand.

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We are given:

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

We can use variable substitution to solve this...