Question

what is the indefinite integral of

4sec4x .tan4x.sec^4 4x dx; u = sec4x
and the other qoustion is integral of (e^4x -4)^1/5 .8e^4x .dx
plz help me

Answer 1

ya that wil work for first question :
u = sec4x

Answer 2

YES U=SEC4X

Answer 3

\[\int8e^{4x}\left(e^{4x}-4\right)^{1/5}~dx\]
Substitute \(u=e^{4x}-4\), then \(\dfrac{1}{4}du=e^{4x}~dx\):
\[2\int u^{1/5}~du\]