# Calculus

posted by Leanna

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

1. MathMate

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

2. Leanna

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

3. bobpursley

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

4. bobpursley

forget that last answer. I am tired.

5. MathMate

For 2, almost, but not quite!
u=√x
du = (1/2)dx/√x
dx/√x = 2du
so
∫sin(√x) dx/√x
=∫sin(u)*2du
=-2cos(u)
=-2cos(√x)

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