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Step-by-step Solution

Integral of 1/((x^2+10)^0.5)

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Answer

$\ln\left|\frac{\sqrt{x^2+10}+x}{\sqrt{10}}\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{dx}{\sqrt{\left(x^2+10\right)}}$
1

Solve the integral $\int\frac{1}{\sqrt{x^2+10}}dx$ by trigonometric substitution using the substitution

$\begin{matrix}x=\sqrt{10}\tan\left(\theta\right) \\ dx=\sqrt{10}\sec\left(\theta\right)^2d\theta\end{matrix}$
2

Substituting in the original integral, we get

$\int\frac{\sqrt{10}\sec\left(\theta\right)^2}{\sqrt{10\tan\left(\theta\right)^2+10}}d\theta$

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Answer

$\ln\left|\frac{\sqrt{x^2+10}+x}{\sqrt{10}}\right|+C_0$
$\int\frac{dx}{\sqrt{\left(x^2+10\right)}}$

Main topic:

Integration by trigonometric substitution

Used formulas:

7. See formulas

Time to solve it:

~ 1.05 seconds