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

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

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