Asked by Leanna
I don't know how to do the integral of e^(lnx^2)dx and the integral of (sin sqrtx)/(sqrtx) dx
Answers
Answered by
MathMate
1. ∫e^(lnx^2)dx
use the identity e^(ln(y)) = y to simplify the expression.
2. try the substitution u=sqrt(x).
use the identity e^(ln(y)) = y to simplify the expression.
2. try the substitution u=sqrt(x).
Answered by
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
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
Answered by
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
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
Answered by
bobpursley
forget that last answer. I am tired.
Answered by
MathMate
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)
Start with:
u=√x
du = (1/2)dx/√x
dx/√x = 2du
so
∫sin(√x) dx/√x
=∫sin(u)*2du
=-2cos(u)
=-2cos(√x)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.