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evaluate ∫ 1/sqrt(x) {1+1/x} dx

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

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