Question

Integrate (e^sqrt(x))/sqrt(x) dx

Answer 1

\[\int \dfrac{e^\sqrt{x}}{\sqrt{x}} dx\]USe U-substitution.
Let \(u = \sqrt x\), \(du = \dfrac{1}{2\sqrt{x}}\Rightarrow 2du = \dfrac{dx}{\sqrt{x}}\)

\[\int \dfrac{e^\sqrt{x}}{\sqrt{x}} dx = 2\int e^u du\]

Answer 2

At du = ... there is suppose to be dx in numerator, not just 1. Sorry.

Answer 3

Is this clear? @Idealist

Answer 4

So the answer is 2e^sqrt(x)+C, right?

Answer 5

lol good job

Answer 6

Thank you.

Answer 7

Glad I helped.