Question

Solve the integral:
sin^3(x) * cos^5(x)
Which trigonometric rule(s) do you use and how?

Answer 1

from looking at this i might actually lop off one of the sine's

Answer 2

maybe write it like this: sin^2(x)cos^5(x)sin(x), then i am sure you can use the Pythagorean identity

Answer 3

Substitute \(t = \sin^2x\) \[dx = \frac{dt}{2\sin x \cos x}\]

Answer 4

\[\int \frac{t* \cancel{\cos x * \sin x } (\cos^2 x)^2}{2 \cancel{\sin x * \cos x}}dt\]

Answer 5

\[\int \frac{t ( 1 - t)^2}{2}dt\]

Answer 6

\[\frac{1}{2}* ( \int (t^3 + t - 2t^2)dt)\]

Answer 7

simpler is always better :) unless you need the practice

Answer 8

Indeed :)

Answer 9

there are many ways to skin a cat

Answer 10

;) Thanks