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Step-by-step Solution

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

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Answer

$2\sqrt{x^2+1}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{2x}{\sqrt{x^2+1}}dx$
1

Taking the constant out of the integral

$2\int\frac{x}{\sqrt{x^2+1}}dx$
2

Solve the integral $\int\frac{x}{\sqrt{x^2+1}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^2+1 \\ du=2xdx\end{matrix}$

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Answer

$2\sqrt{x^2+1}+C_0$
$\int\frac{2x}{\sqrt{x^2+1}}dx$

Main topic:

Integrals of Rational Functions

Used formulas:

3. See formulas

Time to solve it:

~ 0.96 seconds

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