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

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

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