Question

integration
$\: integrate \: x \sqrt{x + a} dx$
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Answer 1

Step-by-step explanation:

$\int \: x \sqrt{x + a} dx \\ let \: x + a = t \\ \frac{dx}{dt} = 1 \\ \int \: (t - a) \sqrt{t} dt \\ \int \: {t}^{ \frac{3}{2} - a \sqrt{t} } dt \\ \frac{2 {t}^{ \frac{5}{2} } }{5} - \frac{2a {t}^{ \frac{3}{2} } }{3} + c \\ put \: t = x + a \\ \frac{2 {(x + a)}^{ \frac{5}{2} } }{5} - \frac{2a {(x + a)}^{ \frac{3}{2} } }{3} + c$