Question

integration of x+1/√2x+3​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{x + 1}{ \sqrt{2x + 3} }dx$

$= \frac{1}{2} \int \frac{2x + 3 - 1}{ \sqrt{2x + 3} }dx$

$= \frac{1}{2} \int \frac{2x + 3 }{ \sqrt{2x + 3} }dx - \frac{1}{2} \int \frac{dx}{ \sqrt{2x + 3} }$

$= \frac{1}{2} \int \sqrt{2x + 3}dx - \frac{1}{2} \int \frac{dx}{ \sqrt{2x + 3} }$

$= \frac{1}{2} \times \frac{2}{3} (2x + 3)^{ \frac{3}{2} } - \frac{1}{2} \times 4 \sqrt{2x + 3} + c$

$= \frac{1}{3} (2x + 3)^{ \frac{3}{2} } - 2 \sqrt{2x + 3} + c$