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Step-by-step Solution

Integral of $\frac{1}{\left(25+16x^2\right)^2}$ with respect to x

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Answer

$\frac{1}{1000}arctan\left(\frac{4}{5}x\right)+\frac{\frac{1}{50}x}{25+16x^2}+C_0$

Step-by-step explanation

Problem to solve:

$\int\:\frac{1}{\left(25+16x^2\right)^2}dx$
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First, factor the terms inside the radical for an easier handling

$\int\frac{1}{\left(16\left(\frac{25}{16}+x^2\right)\right)^2}dx$
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Taking the constant out of the radical

$\int\frac{1}{256\left(\frac{25}{16}+x^2\right)^2}dx$

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Answer

$\frac{1}{1000}arctan\left(\frac{4}{5}x\right)+\frac{\frac{1}{50}x}{25+16x^2}+C_0$