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Step-by-step Solution

Integral of x(2x^2+1)^6

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Answer

$\frac{1}{28}\left(2x^2+1\right)^{7}+C_0$

Step-by-step explanation

Problem to solve:

$\int x\left(2x^2+1\right)^6dx$
1

Solve the integral $\int x\left(2x^2+1\right)^6dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=2x^2+1 \\ du=4xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{4x}=dx$

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Answer

$\frac{1}{28}\left(2x^2+1\right)^{7}+C_0$
$\int x\left(2x^2+1\right)^6dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 1.14 seconds