Integral Calculus> integrate the following integral ∫ (2 – 3...

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

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