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\int\frac{2x^3+7x^2+2x+9}{2x+3}dx

Integral of (2x+9+7x^2+2x^3)/(2x+3)

Answer

$\frac{1}{3}\int\frac{9+2\sqrt[3]{u}+7\sqrt[3]{u^{2}}+2u}{\sqrt[3]{u^{2}}\left(3+2\sqrt[3]{u}\right)}du$

Step-by-step explanation

Problem

$\int\frac{2x^3+7x^2+2x+9}{2x+3}dx$
1

Solve the integral $\int\frac{9+2x+7x^2+2x^3}{3+2x}dx$ applying u-substitution. Let $u$ and $du$ be

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

Unlock this step-by-step solution!

Answer

$\frac{1}{3}\int\frac{9+2\sqrt[3]{u}+7\sqrt[3]{u^{2}}+2u}{\sqrt[3]{u^{2}}\left(3+2\sqrt[3]{u}\right)}du$
$\int\frac{2x^3+7x^2+2x+9}{2x+3}dx$

Main topic:

Integration by substitution

Used formulas:

4. See formulas

Time to solve it:

1.34 seconds