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Step-by-step Solution

Integrate (x/2+3)^2

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Answer

$\frac{2}{3}\left(\frac{x}{2}+3\right)^{3}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(\frac{x}{2}+3\right)^2dx$
1

Solve the integral $\int\left(\frac{x}{2}+3\right)^2dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=\frac{x}{2}+3 \\ du=0.5dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{0.5}=dx$

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Answer

$\frac{2}{3}\left(\frac{x}{2}+3\right)^{3}+C_0$
$\int\left(\frac{x}{2}+3\right)^2dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.85 seconds

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