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Step-by-step Solution

Integrate x/(2+x^2) from 0 to 4

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Answer

$\frac{23}{\sqrt[3]{2}}$

Step-by-step explanation

Problem to solve:

$\int_{0}^{4}\frac{x}{2+x^2}dx$
1

Solve the integral $\int_{0}^{4}\frac{x}{2+x^2}dx$ applying u-substitution. Let $u$ and $du$ be

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

Isolate $dx$ in the previous equation

$\frac{du}{2x}=dx$

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Answer

$\frac{23}{\sqrt[3]{2}}$

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$\int_{0}^{4}\frac{x}{2+x^2}dx$

Main topic:

Integration by substitution

Used formulas:

3. See formulas

Time to solve it:

~ 0.56 seconds