# Evaluate \int \frac{5x^3 + 50x + 25}{x^4 + 25x^2} dx.

## Question:

Evaluate {eq}\int \frac{5x^3 + 50x + 25}{x^4 + 25x^2} dx. {/eq}

## Indefinite Integration.

Most of the question needs substitution of the term for integrating. Substitution makes the problem of integration easy and reduce its complexity. The main task is to choose the term for integration.

## Answer and Explanation:

Expand

{eq}5(\int \frac{x^3+10x+5} {x^2(x^2+25)}dx) {/eq}

Perform partial fraction decomposition,

{eq}5(\int \frac{3x-1}{5(x^2+25)}dx+\int...

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Indefinite Integral: Definition, Rules & Examples

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