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Integral Calculus> evaluate ∫ 1/sqrt(x) {1+1/x} dx...

question mark

evaluate
∫ 1/sqrt(x) {1+1/x} dx

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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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