Question

How do you find the indefinite integral of `int (cosx)/(7sin(x)+42)dx`?

Answer 1

`1/7ln(sinx+6)`

Explanation:

Start by moving any constants outside of the integral. In this case we can pull out `1/7`.

`1/7intcosx/(sinx+6)dx`

We can use substitution to simplify the integral.

`u=sinx+6->du=cosx dx`

Plugging `u` and `du` in the integral simplifies to;

`1/7int1/udu`

The integral of `1/x` is `ln|x| +C`.

`1/7ln|u|+C`

Undoing our earlier substitution, we get the solution to our integral.

`1/7ln|sinx+6|+C`