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Step-by-step Solution

Integrate (3x+2)^0.5

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Answer

$\frac{2}{9}\sqrt{\left(3x+2\right)^{3}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\sqrt{3x+2}dx$
1

Solve the integral $\int\sqrt{3x+2}dx$ applying u-substitution. Let $u$ and $du$ be

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

Isolate $dx$ in the previous equation

$\frac{du}{3}=dx$

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Answer

$\frac{2}{9}\sqrt{\left(3x+2\right)^{3}}+C_0$
$\int\sqrt{3x+2}dx$

Main topic:

Integration by substitution

Time to solve it:

~ 2.1 seconds