Integral Calculus> integrate the following integral ∫ (2x + ...

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

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 11 Years ago

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

$I = \int \frac{2x+1}{\sqrt{3x+2}}dx$
$I = 2\int \frac{x+\frac{1}{2}}{\sqrt{3x+2}}dx$
$I = \frac{2}{3}\int \frac{3x+\frac{3}{2}}{\sqrt{3x+2}}dx$
$I = \frac{2}{3}\int \frac{3x+2-\frac{1}{2}}{\sqrt{3x+2}}dx$
$I = \frac{2}{3}\int \sqrt{3x+2}dx-\frac{1}{3}\int \frac{1}{\sqrt{3x+2}}dx$
$I = \frac{2}{3}\frac{2(3x+2)^{3/2}}{3.3}-\frac{1}{3}\int \frac{1}{\sqrt{3x+2}}dx$
$I = \frac{4(3x+2)^{3/2}}{27}-\frac{2\sqrt{3x+2}}{9}+c$