Calculus

I don't know how to do the integral of e^(lnx^2)dx and the integral of (sin sqrtx)/(sqrtx) dx

asked by Leanna
  1. 1. ∫e^(lnx^2)dx
    use the identity e^(ln(y)) = y to simplify the expression.
    2. try the substitution u=sqrt(x).

    posted by MathMate
  2. Thanks for help on 1.

    on 2. if i do u=sqrt(x) my du is 1/2x^(-1/2) and that means my du is in the denominator. So it would read 2integral of sin(u)/du

    posted by Leanna
  3. Nope, not on two.

    You cant solve it that way easily.

    This is difficult. Brake the sin function into its series equivalent, and integrate the series.

    http://reference.wolfram.com/mathematica/ref/SinIntegral.html

    posted by bobpursley
  4. forget that last answer. I am tired.

    posted by bobpursley
  5. For 2, almost, but not quite!
    Start with:
    u=√x
    du = (1/2)dx/√x
    dx/√x = 2du
    so
    ∫sin(√x) dx/√x
    =∫sin(u)*2du
    =-2cos(u)
    =-2cos(√x)

    posted by MathMate

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