Evaluate: `int1/(cos^6x+sin^6x)\ dx`

Explanation

`I=int frac{d x}{cos ^{6} x+sin ^{6} x}=int frac{sec ^{6} x}{1+tan ^{6} x} d x `


`implies int frac{(1+tan ^{2} x)^{2} sec ^{2} x d x}{1+tan ^{6} x}`


If `tan x=p`,


then `sec ^{2} x d x=d p`


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