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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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

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