The correct option is A x/3(2x+3)^3/2 1/15(2x+3)^5/2+c∫ x(2x+3)^1/2dx =x(2x+3)^3/2/3/21/2 ∫(2x+3)^3/2/3/21/2dx+c =1/3x(2x+3)^3/2 1/15(2x+3)^5/2+c ...

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Definite Integrals

∫ x √2 x+3 d ...

Question

$\int x \sqrt{2 x + 3} d x =$

\frac{x}{3} (2 x + 3)^{3 / 2} - \frac{1}{15} (2 x + 3)^{5 / 2} + c

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\frac{x}{3} (2 x + 3)^{3 / 2} + \frac{1}{15} (2 x + 3)^{5 / 2} + c

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\frac{x}{3} (2 x + 3)^{3 / 2} + \frac{1}{6} (2 x + 3)^{5 / 2} + c

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None of these

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Solution

The correct option is A $\frac{x}{3} (2 x + 3)^{3 / 2} - \frac{1}{15} (2 x + 3)^{5 / 2} + c$
$\int x (2 x + 3)^{1 / 2} d x = x \frac{(2 x + 3)^{3 / 2}}{\frac{3}{2}} \frac{1}{2} - \int \frac{(2 x + 3)^{3 / 2}}{\frac{3}{2}} \frac{1}{2} d x + c = \frac{1}{3} x (2 x + 3)^{3 / 2} - \frac{1}{15} (2 x + 3)^{5 / 2} + c$

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