Posted by **MathisFrustrating** on Monday, May 2, 2011 at 10:41pm.

Evaluate integral of e^x^(1/2) / x^(1/2)

I've looked at the answer but I don't understand what people do in their steps.

When I substitute x^(1/2) for u, I get:

2du = 1/x^(1/2) dx

But what do you do with the 1/x^(1/2) dx? It just disappears in the solutions I've seen people give.

- calculus -
**Jai**, Monday, May 2, 2011 at 10:59pm
yes. the substitution is correct:

let u = x^(1/2)

thus du = 1/[2(x^(1/2))] dx, or

dx = 2(x^(1/2)) du, or

dx = 2u du

substituting these to original integral,

integral of [e^x^(1/2) / x^(1/2)] dx

integral of [(e^u) / u] * (2u) du

the u's will cancel out:

integral of [2*e^u] du

we can readily integrate this to

2*e^u + C

substituting back the value of u,

2*e^(x^(1/2)) + C

hope this helps~ :)

- calculus -
**MathisFrustrating**, Monday, May 2, 2011 at 11:33pm
This helped alot :)

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