Expert: Ahmed Salami - 1/29/2006

Question
Integrate by part with respect to x:

(x^5)*(e)^(x^3).

Please list the exponent integration used in solving this problem.  

Answer
Hi Farooq,
Sorry for the time it took. Technical problem with the site.
To find the integral of x^5 . e^(x^3)
We use the substitution u = x^3, du = 3x^2 dx
The integral $x^5.e^(x^3) dx then becomes
$x^5.e^u.du/3x^2 = $x^3.e^u.du/3
= (1/3)$u(e^u) du
integrating by parts by taking v = e^u
the final solution becomes (1/3)(e^u)(u-1)
i.e (1/3).e^(x^3).(x^3 - 1)
Let me know if any part of it is not clear.
I hope i have helped. You can always get back to me.
Regards.