Thread: Integration of ∫e^(1/2t) t^2

How do you integrate ∫[e^(1/2t) t^2]?

Is this done by parts? I've been away from calculus for about 7 years now...I've been looking through my Calc book but I can't remember very much of this stuff and how to decide what to use to integrate what.

∫e^(1/2t) t^2

Use integration by parts twice.

u=t^2 ----- v=e^(1/2t)

ah great! thanks

Thanks for the help, how does this look?

1st time by parts:

u = t^2 dv = e^(1/2t) dt
du = 2t dt v = 2e^(1/2t)

uv - Int v du
= (t^2)(2e^(1/2t)) - Int [2e^(1/2t)](2t) dt

2nd time by parts:

u = 2t dv = 2e^(1/2t)
du = 2t dt v = 4e^(1/2t) dt

uv - Int v du
= (2t)(4e^(1/2)) - Int (4e^(1/2t))*2 dt
= (2t)(4e^(1/2)) - 8*(2e^(1/2t)
= (2t)(4e^(1/2)) - 16 e^(1/2t)

Also, sorry but does anyone know where I can find the explanation page? I'm trying to figure out how to display the Integral sign and exponents properly.

Many thanks

nm, got it

Originally Posted by crabchef

Also, sorry but does anyone know where I can find the explanation page? I'm trying to figure out how to display the Integral sign and exponents properly.

Many thanks

Look around here: http://www.mathhelpforum.com/math-help/latex-help/

Good luck