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 :)
Answer This Question
Related Questions
 calculus I integral  Is this correct? Evaluate 2x∫1 3t(t^2 + 1)^2 dt u= t...
 Calculus  First make a substitution and then use integration by parts to ...
 Calculus  First make a substitution and then use integration by parts to ...
 Calculus  integral 0 to sqrt(3) dx/sqrt(4x^2) I don't understand why the ...
 Calculus  S=Integral xdx/sqrt(x1). I have proceeded thus Put sqrt(x1)=u then...
 Calculus  I'm not sure what to substitute in this question. Evaluate the ...
 calculus  a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write...
 Calculus 2  I'm confused on how to solve or set up a substitute for the problem...
 Calculus  Can someone look over my work and tell me if my steps look correct? I...
 Calculus  Instructions were evaluate the integral. (x/1x^4) dx I know that ...
More Related Questions