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Step-by-step Solution

Integral of 4/((x^2+4)^1.5)

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Answer

$\frac{x}{\sqrt{x^2+4}}+C_0$

Step-by-step explanation

Problem to solve:

$\int \frac { 4 d x } { ( x ^ { 2 } + 4 ) ^ { 3 / 2 } }$
1

Solve the integral $\int\frac{4}{\sqrt{\left(x^2+4\right)^{3}}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=2\tan\left(\theta\right) \\ dx=2\sec\left(\theta\right)^2d\theta\end{matrix}$
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Substituting in the original integral, we get

$\int\frac{8\sec\left(\theta\right)^2}{\sqrt{\left(4\tan\left(\theta\right)^2+4\right)^{3}}}d\theta$

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Answer

$\frac{x}{\sqrt{x^2+4}}+C_0$
$\int \frac { 4 d x } { ( x ^ { 2 } + 4 ) ^ { 3 / 2 } }$

Main topic:

Integration by trigonometric substitution

Used formulas:

7. See formulas

Time to solve it:

~ 1.01 seconds

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