Integral Calculus> integrate the following integral ∫ (x + 1...

integrate the following integral
∫ (x + 1) / sqrt(2x + 3) dx

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{x+1}{\sqrt{2x+3}}dx$
$I = \frac{1}{2}\int \frac{2x+2}{\sqrt{2x+3}}dx$
$I = \frac{1}{2}\int \frac{2x+3-1}{\sqrt{2x+3}}dx$
$I = \frac{1}{2}\int [\sqrt{2x+3}-\frac{1}{\sqrt{2x+3}}]dx$
$I = \frac{1}{2}\int \sqrt{2x+3}dx-\frac{1}{2}\int \frac{1}{\sqrt{2x+3}}dx$
$I = \frac{(2x+3)^{3/2}}{3}-\frac{1}{2}\int \frac{1}{\sqrt{2x+3}}dx$
$I = \frac{(2x+3)^{3/2}}{3}-\frac{1}{2}\sqrt{2x+3}+c$