>>12192094Let sinx = sqrt(1-cos^2x), then we have (tanx)^(1/2)/((1+cos^2x)^(3/4)), and then we have the original integrand with an extra factor of (1/sqrt(cosx)) and the denominator raised to the 3/4 power. Repeat the process again and we have the integral of (1/cosx) sqrt(sinx/1+cos^2x). Repeat again twice and we have the integral of 1/cos^2x.
Thus this integral is equivalent to integrating sec^2x. And since the derivative of tangent is sec2x, we have that your integral is equal to tan(pi)-tan(0)=0
