Question

Compute the following indefinite integral (7x^4)*(E^X^5)*dx

Answer 1

\[\int\limits 7x^4 e ^{x ^{5}}dx\]
put x^5=t
\[5x^4 dx=dt,x^4~dx=\frac{ 1 }{ 5 }dt\]
complete it.

Answer 2

I'm really confused...I understand \[x^5=t\] and \[dt=5x^4dx\] but I don't understand \[x^4dx=1/5dt\]. This part is confusing on my printed notes as well and its the only part I seem to see.

Answer 3

Ok. I just figured that piece out. But I'm confused on how to put it all together.

Answer 4

I think I got it. This is really a lot of substitution essentially and keeping track of alot of little things.
\[7(1/5dt(e^t))\]

7/5*e^(x^5)+c
Thanks