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

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

Grade:12

1 Answers

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

I = \int \frac{1}{\sqrt{x}(\sqrt{x}+1)}dx
\sqrt{x} + 1 = t
\frac{1}{2\sqrt{x}}dx = dt
I = \int \frac{2}{t}dt
I = 2log(t) + c
I = 2log(\sqrt{x}+1) + c

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