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evaluate ∫ e^(log(sqrt(x))) / x dx

evaluate    ∫ e^(log(sqrt(x))) / x  dx

Grade:12

1 Answers

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

I = \int \frac{e^{log\sqrt{x}}}{x}dx
log\sqrt{x} = t
\frac{1}{\sqrt{x}}.\frac{1}{2\sqrt{x}}dx = dt
\frac{dx}{x} = 2dt
I = \int 2e^{t}dt
I = 2e^{t} + constant
I = 2e^{log(\sqrt{x})} + constant

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