Homework Help: Calculus

Posted by Leanna on Monday, April 11, 2011 at 10:25pm.

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

Calculus - MathMate, Monday, April 11, 2011 at 10:44pm
1. ∫e^(lnx^2)dx
use the identity e^(ln(y)) = y to simplify the expression.
2. try the substitution u=sqrt(x).
Calculus - Leanna, Monday, April 11, 2011 at 11:00pm
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
Calculus - bobpursley, Tuesday, April 12, 2011 at 12:27am
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
Calculus - bobpursley, Tuesday, April 12, 2011 at 12:28am
forget that last answer. I am tired.
Calculus - MathMate, Tuesday, April 12, 2011 at 5:14am
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)

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