Evaluate: `int_0^pi(x dx)/(1+cosalphasinx),w h e r e0

Evaluate int_(0)^(pi)(xdx)/(1+cosalphasinx),0ltalphaltpi .

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Evaluate int_(0)^(2)e^(x)dx

Evaluate: int_(0)^(2 pi)(1)/(1+e^(sin x))dx

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Evaluate: (int0n[x]dx)/(int0n{x}dx)(w h e r e[x]a n d{x} are integral and fractional parts of xa n dn in N)dot

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