Question

integration ofsin^7x*cosx

Answer 1

u= sin(x)

Answer 2

the derivative is in there. sitting.

Answer 3

there is a very obvious u substitution

Answer 4

you know though, that \(\large\color{black}{ \sin^7(x) }\) is the same thing as \(\large\color{black}{ ( \sin x)^7 }\).
And that,

\(\large\color{black}{ \frac{d}{dx}~\sin(x)=\cos(x) }\)

Answer 5

you are not replying, but I'll ask you this. Have you ever done u-substitution before (because it really looks like a u-substitution problem, or are you just testing the function by "where it's coming from" saying "what could be the derivative from which this sin^7xcosx can come" ?