Find the error in steps to evaluate the following integral

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Find the error in steps to evaluate the following integral. ∫0πdx1+2sin⁡2x=∫0πsec⁡2xdxsec⁡2x+2tan⁡2x=∫0πsec⁡2xdx1+3tan⁡2x\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} =13[tan⁡−1(3tan⁡x)]0π=0= \frac{1}{\sqrt{3}} [\tan^{-1}(\sqrt{3} \tan x)]_{0}^{\pi} = 0

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