# Evaluate the indefinite integral `int sin(83x)*cos^(1/3)(83x)dx`

*print*Print*list*Cite

### 1 Answer

The integral `int sin(83x)*cos^(1/3)(83x)dx` has to be determined.

Let cos(83*x) = y

=> `dy = -83*sin (83*x) dx`

=> `(-1/83) dy = sin(83*x) dx`

`int sin(83x)*cos^(1/3)(83x)dx`

=> `(-1/83)*int y^(1/3) dy`

=> `(-3/332)*y^(4/3)`

substitute y = cos(83*x)

=> `(-3/332)*cos^(4/3)(83*x) + C`

**The integral `int sin(83x)*cos^(1/3)(83x)dx` = `(-3/332)*cos^(4/3)(83*x) + C` **