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evaluate ∫ (1 + sqrt(x))^2/sqrt(x) dx

evaluate
∫ (1 + sqrt(x))^2/sqrt(x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
I = \int \frac{(1+\sqrt{x})^{2}}{\sqrt{x}}dx
I = \int \frac{(1+x+2\sqrt{x})}{\sqrt{x}}dx
I = \int (x^{-1/2}+\sqrt{x}+2)dx
I = \int x^{-1/2}dx+\int \sqrt{x}+\int 2dx
I = 2\sqrt{x}+\frac{2x^{3/2}}{3}+2x+c

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