Ok the original problem is
Integral sin^(4) x cos^(4) x
After making the two of those sin^2 and and cos^2 and doing trig function substation my integral became
1/4 integral [1-cos^2 2x]^2
Then 1/4 [sin^2 2x]^2
I am officially I stuck and I know I'm close to solving it but I am now waving the white flag
Please help!
You can check the answer here:
int (sin(x))^4 (cos(x))^4 - Wolfram|Alpha