Question :
$\displaystyle \frac{dx}{(1+x)\sqrt{x}}$
Please answer in steps
Thank you
Hello, mj.alawami!
$\displaystyle \frac{dx}{(1+x)\sqrt{x}}$
Let: .$\displaystyle u \,=\,\sqrt{x} \quad\Rightarrow\quad x \,=\,u^2\quad\Rightarrow\quad dx \,=\,2u\,du$
Substitute: .$\displaystyle \int\frac{2u\,du}{(1+u^2)\,u} \;=\;2\!\!\int\!\frac{du}{1+u^2} \;=\; 2\arctan u + C$
Back-substitute: .$\displaystyle 2\arctan\left(\sqrt{x}\right) + C$