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calculus

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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 -

    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 -

    This helped alot :)

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