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

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

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