Mathematics

Evaluate the given integral.
$$\displaystyle\int{\dfrac{dx}{{x}^{\frac{3}{2}}}}$$


SOLUTION
$$I=\displaystyle\int{\dfrac{dx}{{x}^{\frac{3}{2}}}}$$

$$=\displaystyle\int{{x}^{-\frac{3}{2}}dx}$$

$$=\dfrac{{x}^{-\frac{3}{2}+1}}{-\dfrac{3}{2}+1}+c$$

$$=\dfrac{{x}^{\frac{-3+2}{2}}}{\dfrac{-3+2}{2}}+c$$

$$=\dfrac{{x}^{\frac{-1}{2}}}{\dfrac{-1}{2}}+c$$

$$=\dfrac{-2}{\sqrt{x}}+c$$
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Subjective Medium Published on 17th 09, 2020
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