Integral over a symmetric interval of 1/((1 + e^(odd function))(sin^n x + cos^n x))

The same question, asked 2 times: 2021 Paper 16*, 14 Jun 2022. Every wording below, oldest first.

Try each one first, then open its answer.

Question 1
2021 Paper 16
44 $\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \frac{dx}{\left( 1 +e^{xcosx} \right)\left( \sin^{4}x+\cos^{4}x \right)}$
Tap an option to check your answer.
Question 2
14 Jun 2022
156 $\int_{-\pi/2}^{\pi/2} \frac{dx}{\left( 1 +e^{x} \right)\left( \sin^{6}x+\cos^{6}x \right)}$
Tap an option to check your answer.