Mathematics

Problem

Find the error in steps to evaluate the following integral.

\int_{0}^{\pi} \frac{dx}{1+2\sin^2 x} = \int_{0}^{\pi} \frac{\sec^2 x dx}{\sec^2 x + 2 \tan^2 x} = \int_{0}^{\pi} \frac{\sec^2 x dx}{1+3 \tan^2 x}

= \frac{1}{\sqrt{3}} [\tan^{-1}(\sqrt{3} \tan x)]_{0}^{\pi} = 0