`int sin^(3)x cos x dx` किसके बराबर है ?

Options

A. `cos^(2) x + C`
B. `sin^(4) x + C`
C. `((1-sin^(2)x)^(2))/(4) + C`
D. `((1-cos^(2)x)^(2))/(4) + C`

Explanation

दिया है,
`intsin^(3)x cos x dx`
माना `sinx = t`
`cos x dx = dt`
`= intt^(3) dt = (t^(2))/(4) + C`
`(sin^(2)x)/(4) + C = ((sin^(2)x))/(4)+ C`
`=((1-cos^(2)x)^(2))/(4) + C`
`[ :' sin^(2)x + cos^(2) x - 1 ]`