# Is everything clear about integrals of sines and cosines?

Calculus Level 4

$\large \int \dfrac{\sin^2x \cos^2x }{(\sin^3x+\cos^3x)^2} \, dx$

The indefinite integral above is equal to

$-\dfrac{1}{3}\frac{\cos^3 x}{(A\cos x+B\sin x)(1-\sin x \cos x)}+C$

for constants $$A$$ and $$B$$, where $$C$$ denotes the arbitrary constant of integration. Find the value of $$A+B$$.

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