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

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

Grade:12

1 Answers

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

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

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