Question

Integrate (sin x)^6 please

Answer 1

Formula is:
`\int {sin^(n) x} \, dx =- (1)/(n)sin^(n-1)x cos x + (n-1)/(n) \int {sin^(n-2) x} \, dx`
We will use it here:
`\int {sin^(6) x} \, dx =- (1)/(6) sin^(5)xcosx+ (5)/(6) \int{sin^(4)x } \, dx`
And again:
`\int {sin^(4) x} \, dx =- (1)/(2) sin^(3) xcosx+ (3)/(4) \int{sin^(2)x } \, dx`
Finally:
`\int {sin^(2)x } \, dx=- (1)/(2)sinx cos x+ (1)/(2)`
The result:
`=- (1)/(6) sin^(5) xcosx- (5)/(24)sin^(3)xcosx- (15)/(48)sinxcosx+ (15)/(48)+C`
Thank you.