# Math Help - Integral Help!

1. ## Integral Help!

Hey, can you show me how to do the integral for this question

(t^2)(e^(-t^3)

Thanks

2. Originally Posted by Mudd_101
Hey, can you show me how to do the integral for this question

(t^2)(e^(-t^3)

Thanks
Using the substitution $u=-t^3$, I leave it for you to show that $\int t^2e^{-t^3}\,dt\xrightarrow{u=-t^3}{}-\tfrac{1}{3}\int e^u\,du$

Can you continue with the calculations?

3. I almost got the answer but I'm negative off uhh I put my steps down their if you could Pleaassse look at them but uhh I'm new to integrals so I think they will be difficult to follow cuz I don't really know what I'm doing.

okay so I have t^2 e^u

u = -t^3
-3t^2 dt = du
t^2 dt= (-1/3)du

so then I have: (-1/3)du *e^u
then I did the integral of e^u (leaving behind the -1/3 from the du)
(-1/3) ((e^(-t^3))/(-1))

The answer in my text is (-1/3)((e^(-t^3))

4. Originally Posted by Mudd_101
I almost got the answer but I'm negative off uhh I put my steps down their if you could Pleaassse look at them but uhh I'm new to integrals so I think they will be difficult to follow cuz I don't really know what I'm doing.

okay so I have t^2 e^u

u = -t^3
-3t^2 dt = du
t^2 dt= (-1/3)du

so then I have: (-1/3)du *e^u
then I did the integral of e^u (leaving behind the -1/3 from the du)
(-1/3) ((e^(-t^3))/(-1))

The answer in my text is (-1/3)((e^(-t^3))
I'm not sure how you got that -1...

When you evaluate $-\tfrac{1}{3}\int e^u\,du$, you end up with $-\tfrac{1}{3}e^u+C$. Now back substitute to get $\boxed{-\tfrac{1}{3}e^{-t^3}+C}$

5. ooo thanks