Step-by-step Solution

Integrate x(2x+5)^10

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$\frac{1}{48}\left(2x+5\right)^{12}-\frac{5}{44}\left(2x+5\right)^{11}+C_0$

Step-by-step explanation

Problem to solve:

$\int\:x\:\left(2x+5\right)^{10}dx$
1

Solve the integral $\int x\left(2x+5\right)^{10}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=2x+5 \\ du=2dx\end{matrix}$
2

Isolate $dx$ in the previous equation

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

$\frac{1}{48}\left(2x+5\right)^{12}-\frac{5}{44}\left(2x+5\right)^{11}+C_0$
$\int\:x\:\left(2x+5\right)^{10}dx$