Question

Evaluate the indefinite integral.

Answer 1

\[\int\limits \sin ^{3}x \cos x dx\]

Answer 2

Hmm so what are you thinking? :x
U-sub maybe?

Answer 3

yea would u be sin^3x or cos x?

Answer 4

\[\Large\bf\sf \int\limits (\sin x)^3\left(\cos x \;dx\right)\]Maybe this will make it easier to see your substitution that you need to make.
You're looking for something and it's derivative.

sin^3x doesn't give us cosx when we take it's derivative. Hmm that won't work.

Answer 5

Cosine when we take it's derivative gives us -sine.
But that only deals with one of the powers of sine.

Any other ideas? :o

Answer 6

do i distribute or use an identity?

Answer 7

No.

Answer 8

\[\Large\bf\sf \int\limits\limits (\color{orangered}{\sin x})^3\left(\color{royalblue}{\cos x \;dx}\right)\]

\[\Large\bf\sf \color{orangered}{u=\sin x},\qquad\qquad\qquad \color{royalblue}{du=?}\]

Answer 9

cos x

Answer 10

cos x dx

Answer 11

\[\Large\bf\sf \color{orangered}{u=\sin x},\qquad\qquad\qquad \color{royalblue}{du=\cos x dx}\]Yup sounds right.

Answer 12

\[\Large\bf\sf \int\limits\limits\limits (\color{orangered}{\sin x})^3\left(\color{royalblue}{\cos x \;dx}\right)\quad=\quad \int\limits\limits\limits (\color{orangered}{u})^3\left(\color{royalblue}{du}\right)\]It's a pretty simple problem right? :o
Maybe the trig was just confusing you.

Answer 13

thank you