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Find the mistake in the following evalua...

Find the mistake in the following evaluation of the integral `I=int_0^pi(dx)/(1+2sin^2x)`, then : `I=int_0^pi(dx)/(cos^2x+3sin^2x)` `=int_0^pi(sec^2x dx)/(1+3tan^2x)=1/(sqrt(3))[tan^(-1)(sqrt(3)tanx)]_pi^0=0`

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