Question

I need a step by step guide for this problem:

integrate e^(t^2) * t^3

Answer 1

you could try a subsitution
u=t^2

Answer 2

recall by law of exponents you can write t^3 as t^2*t

Answer 3

Correct, resulting in \[(1/2) \int\limits_{}^{}e^u * u du\]

Answer 4

then integration by parts

Answer 5

How does that go?

Answer 6

do you know the product rule for derivatives?

Answer 7

yes, (F*G)' = F'*G + F*G'

Answer 8

\[(fg)'=f'g+fg' \\ \text{ integrate both sides } \\ fg=\int\limits_{}^{}f'g dx+\int\limits_{}^{}fg'dx \\ fg-\int\limits_{}^{}f'gdx=\int\limits_{}^{}fg' dx\]

Answer 9

choose f to be u and choose g' to be e^u

Answer 10

\[\int\limits_{}^{}fg' du=fg-\int\limits_{}^{}f' g du\]
f=u g'=e^u
f'=? g=?

Answer 11

have you not learned integration by parts yet?

Answer 12

if so I don't know another way to do the integral

Answer 13

My physics friend was able to finish off the question. Thank you for getting me started.