Question

Integrate sin3x/4-cos3x dx=?

Answer 1

`1/3ln|(4-cos3x)|+C.`

Explanation:

If we subst. `y=(4-cos3x)`, then, `dy=-(-sin3x)*3dx`.

`:. intsin3x/(4-cos3x)=1/3int(3sin3x)/(4-cos3x)dx=1/3int1/ydy`,

`=1/3ln|y|`,

`=1/3ln|(4-cos3x)|+C.`