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.

Printable View

- June 29th 2010, 08:03 AMcrabchefIntegration 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. - June 29th 2010, 08:11 AMp0oint
∫e^(1/2t) t^2

Use integration by parts twice.

u=t^2 ----- v=e^(1/2t) - June 29th 2010, 08:12 AMcrabchef
ah great! thanks :)

- June 29th 2010, 08:59 AMcrabchef
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 - June 29th 2010, 10:24 AMcrabchef
nm, got it :)

- June 29th 2010, 10:32 AMUlyssesQuote:

Originally Posted by**crabchef**

Good luck ;)