Question

Integradation x^ -3/2 dx​

Answer 1

We have to find,

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

We know that,

$\displaystyle\longrightarrow\sf{\int x^n\ dx=\dfrac{x^{n+1}}{n+1}+c,\ \ n\neq-1}$

Taking $\sf{n=-\dfrac{3}{2},}$

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

$\displaystyle\longrightarrow\sf{I=\dfrac{x^{-\frac{3}{2}+1}}{\left(-\dfrac{3}{2}+1\right)}+c}$

$\displaystyle\longrightarrow\sf{I=\dfrac{x^{-\frac{1}{2}}}{\left(-\dfrac{1}{2}\right)}+c}$

$\displaystyle\longrightarrow\sf{\underline{\underline{I=-2x^{-\frac{1}{2}}+c}}}$

Or,

$\displaystyle\longrightarrow\sf{\underline{\underline{I=-\dfrac{2}{\sqrt x}+c}}}$