Question

find integration of the photo question fast

Answer 1

Step-by-step explanation:

We have,

$\int \frac{x \: dx}{ \sqrt{x + 4} }$

$= \int \frac{(x + 4 - 4)dx}{ \sqrt{x + 4} }$

$= \int( \sqrt{x + 4} - \frac{4}{ \sqrt{x + 4} })dx$

$= \int \sqrt{x + 4} \: dx - 4 \int \frac{dx}{ \sqrt{x + 4} }$

$= \frac{2}{3} (x + 4)^{ \frac{3}{2} } - 4 \times 2 \sqrt{x + 4} + c$

$= \frac{2}{3} (x + 4)^{ \frac{3}{2} } - 8 \sqrt{x + 4} + c$