Evaluate the following integrals: x (3-5x)dx - Vidyadip

Question

Evaluate the following integrals:
$\int\sqrt{\text{x}}(3-5\text{x})\text{dx}$

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Answer

$\int\sqrt{\text{x}}(3-5\text{x})\text{dx}$
$=\int\text{x}^{\frac{1}{2}}(3-5\text{x})\text{dx}$
$=\int\Big(3\text{x}^\frac{1}{2}-5\text{x}^\frac{3}{2}\Big)\text{dx}$
$=3\bigg[\frac{\text{x}^{\frac{1}{2}+1}}{\frac{1}{2}+1}\bigg]-5\bigg[\frac{\text{x}^{\frac{3}{2}+1}}{\frac{3}{2}+1}\bigg]+\text{C}$
$=2\text{x}^{\frac{3}{2}}-2\text{x}^{\frac{5}{2}}+\text{C}$

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