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Step-by-step Solution

Integral of 1/((25+16x^2)^(3/2))

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Answer

$\frac{\frac{1}{25}x}{\sqrt{25+16x^2}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\:\frac{1}{\left(25+16x^2\right)^{\frac{3}{2}}}dx$
1

First, factor the terms inside the radical for an easier handling

$\int\frac{1}{\sqrt{\left(16\left(\frac{25}{16}+x^2\right)\right)^{3}}}dx$
2

Taking the constant out of the radical

$\int\frac{1}{64\sqrt{\left(\frac{25}{16}+x^2\right)^{3}}}dx$

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Answer

$\frac{\frac{1}{25}x}{\sqrt{25+16x^2}}+C_0$
$\int\:\frac{1}{\left(25+16x^2\right)^{\frac{3}{2}}}dx$

Main topic:

Integration by trigonometric substitution

Used formulas:

8. See formulas

Time to solve it:

~ 1.04 seconds