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Question

Solve: $\int \frac{2 x^{4} + 7 x^{3} + 6 x^{2}}{x^{2} + 2 x} d x$

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Solution

$\int \frac{{2 x}^{4} + {7 x}^{3} + 6 x^{2}}{x^{2} + 2 x} d x$
$\Rightarrow \int \frac{x^{2} ({2 x}^{2} + 7 x + 6)}{x (x + 2)} d x$
$\Rightarrow \int \frac{x (2 x + 3) (x + 2)}{(x + 2)} d x$
$\Rightarrow \int ({2 x}^{2} + 3 x) d x$
$\Rightarrow \frac{2}{3} x^{3} + \frac{{3 x}^{2}}{2} + c$

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