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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1}{\sqrt{2x-3}+\sqrt{2x+3}}dx
I = \int \frac{\sqrt{2x+3}-\sqrt{2x-3}}{(\sqrt{2x-3}+\sqrt{2x+3})(\sqrt{2x+3}-\sqrt{2x-3})}dx
I = \int \frac{\sqrt{2x+3}-\sqrt{2x-3}}{6}dx
I = \frac{1}{6}\int \sqrt{2x+3}dx-\frac{1}{6}\int \sqrt{2x-3}dx
I = \frac{(2x+3)^{3/2}}{18}-\frac{(2x-3)^{3/2}}{18}+c

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