Indefinite Integral?

Question

Find the indefinite integral of: cos(x)*sqrt(4-sin(x)) dx


Answer = ? + C

Answer 1

Cos(x) * sqrt(4-sin(x)) dx
u = 4 - sinx
du = cosx
Since du = -cosx, all you need to do is differentiate u^1/2.
The anti-derivative of u^1/2 is 2/3u^3/2, Then you plug in for u.
The answer is -2/3(4-sinx)^3/2

Answer 2

Let u = sin x du = cos x dx. Then we get
∫ √(4-u) du.
= -2/3*(4-u)^3/2 + C = -2/3* (4-sin x)^3/2+ C.

Answer 3

using substitution :

let u=4-sinx
-du=cosx dx
now put it in equation.
du/dx=-2/3u"3/2.

now put u=4-sinx

answer=-2/3(4-sinx)"3/2+c.