Question

x
$intigration\: of \: \: x \sqrt{x + 2}$
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Answer 1

Step-by-step explanation:

We have,

$\int \: x \sqrt{x + 2} dx$

$let \: \: x + 2 = {t}^{2} \\ \implies \: dx = 2tdt$

$= \int( {t}^{2} - 2)2 {t}^{2} dt$

$= \int(2 {t}^{4} - 4 {t}^{2} )dt$

.

$= 2 \int {t}^{4} dt - 4 \int {t}^{2} dt$

$= \frac{2 {t}^{5} }{5} - \frac{4 {t}^{3} }{3} + c$

$= \frac{2}{5} (x + 2)^{ \frac{5}{2} } - \frac{4}{3} (x + 2) ^{ \frac{3}{2} } + c$