Question

Indefinite intergral (x+3)^2sin x dx ?

Answer 1

`-cot-x+C`

Explanation:

`int(1-sin^2(x))/sin^2(x)dx=int1/sin^2(x)-sin^2(x)/sin^2(x)dx`

Use `intf(x)+g(x)dx=intf(x)dx+intg(x)dx`

`int(1)/sin^2(x)dx-intsin^2(x)/sin^2(x)dx=int(1)/sin^2(x)dx-int1dx`

Use `1/sin^2(x)=csc^2(x)`

`intcsc^2(x)dx-int1dx`

The integral of `csc^2(x)` is `-cot(x)`

`-cot(x)-x+C`