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# Step-by-step Solution

## Integral of $\frac{1}{\sqrt{x^2+10}}$ with respect to x

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### Videos

$\mathrm{arcsinh}\left(\frac{x}{3.1623}\right)+C_0$

## Step-by-step explanation

Problem to solve:

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

Apply the integral formula of inverse hyperbolic functions: $\int\frac{1}{\sqrt{x^2+a^2}}dx = \sinh^{-1}\frac{x}{a}$

$\mathrm{arcsinh}\left(\frac{x}{3.1623}\right)$
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As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$\mathrm{arcsinh}\left(\frac{x}{3.1623}\right)+C_0$

$\mathrm{arcsinh}\left(\frac{x}{3.1623}\right)+C_0$

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 1.02 seconds