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

 
integrate the following integral
∫ 1 / sqrt(x + a) + sqrt(x + b) 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{x+a}+\sqrt{x+b}}dx
I = \int \frac{\sqrt{x+a}-\sqrt{x+b}}{(\sqrt{x+a}+\sqrt{x+b})(\sqrt{x+a}-\sqrt{x+b})}dx
I = \int \frac{\sqrt{x+a}-\sqrt{x+b}}{a-b}dx
I = \frac{1}{a-b}[\int \sqrt{x+a}dx-\int \sqrt{x+b}dx]
I = \frac{1}{a-b}[\frac{2(x+a)^{3/2}}{3}-\int \sqrt{x+b}dx]
I = \frac{1}{a-b}[\frac{2(x+a)^{3/2}}{3}-\frac{2(x+b)^{3/2}}{3}]+c
I = \frac{2}{3(a-b)}[(x+a)^{3/2}-(x+b)^{3/2}]+c

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