Urgent Integration Q Help! (1 Viewer)

[Swalbs]

Guys and gals, how do you integrate xe^x?

Looks easy i know, but im stumped..

 

[香港!]

Guys and gals, how do you integrate xe^x?

Looks easy i know, but im stumped..

I=int. xe^x dx
let u=x and dv\dx=e^x
du=dx and v=e^x
.: I=xe^x-e^x+C using 'Integration by Parts'

 

[Hoey]

http://www.math.hmc.edu/calculus/tutorials/int_by_parts/

 

[icycloud]

Integration by parts is part of the 4U syllabus. Integrals of this kind would not be examined in the 3U exam. However, you might be given a lead-in,

e.g. Differentiate xln(x). Hence or otherwise, integrate xe^x.
In which case,

d/dx [xln(x)] = ln(x) + 1
∫ln(x) + 1 dx = xln(x) + C
∫ln(x) dx = xln(x) - x + C

Now, I = ∫xe^x dx
Let u = e^x, du = e^x dx

I = ∫x du
But x = ln(u)
Thus, I = ∫ln(u) du
= uln(u) - u + C (from previous part)
= e^x*ln(e^x) - e^x + C
= xe^x - e^x + C #

 

[Swalbs]

Thx guys, glad this is 4unit only, although i found the Q in a 2unit textbook!

But it was a simpsons rule question, not pure integration, so that wud explain it.



Cheers