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(i) int0^(pi//2) (sin^3x)/(sin^3x+cos^3x...

(i) `int_0^(pi//2) (sin^3x)/(sin^3x+cos^3x) dx`
(ii) `int_0^(pi//2) (cos^3x)/(sin^3x+cos^3x) dx`
(iii) `int_0^(pi//2) (sin^4x)/(sin^4x+cos^4x) dx`
(iv) `int_0^(pi//2) (cos^5x)/(sin^5x+cos^5x) dx`
(v) `int_0^(pi//2) (sin^5x)/(sin^5x+cos^5x) dx`

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