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

Integral of (x/2+3)^2

Answer

$6\left(3+\frac{x}{2}\right)+2x\left(3+\frac{x}{2}\right)+\frac{1}{6}x^2\left(3+\frac{x}{2}\right)+C_0$

Step-by-step explanation

Problem

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

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

$\begin{matrix}u=3+\frac{x}{2} \\ du=\frac{1}{2}dx\end{matrix}$

Unlock this step-by-step solution!

Answer

$6\left(3+\frac{x}{2}\right)+2x\left(3+\frac{x}{2}\right)+\frac{1}{6}x^2\left(3+\frac{x}{2}\right)+C_0$

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

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.56 seconds