Question

Evaluate: $\int\limits^{\pi/4}_0 { \frac{\tan^{3}x}{1+\cos 2x}} \, dx$

Answer 1

Letting x=π2−x and using the property that

∫a0f(x)dx=∫a0f(a−x)dx

we obtain

∫π20tanx(1+(π2−x)2)(1+tanx)dx

Now, add equation (1) and (2). After that I do not understand how I can proceed fυятнєя

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