Question

Calcule a integral ∫√׳ dx

Answer 1

$\Large\displaystyle\text{ \begin{gathered} \tt \int \sqrt{x^3}\ dx=\int x^{\frac{3}{2} }\ dx\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \tt \int x^ndx=\frac{x^{n+1}}{n+1} +C\ ,\ \forall n\neq-1\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \tt \int \sqrt{x^3}\ dx=\frac{x^{\frac{3}{2}+1 }}{\frac{3}{2}+1 } +C\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \tt \int \sqrt{x^3}\ dx=\frac{x^{\frac{5}{2} }}{\frac{5}{2} } +C\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \tt \int \sqrt{x^3}\ dx=\frac{2x^{\frac{5}{2} }}{5 } +C\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \boxed{\tt \int \sqrt{x^3}\ dx=\frac{2\sqrt{x^{5}}}{5 } +C\ ,\ C\in \mathbb{R}}\end{gathered} }$