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If $\int_{0}^{π / 4} \frac{x \sin x}{\cos^{3} x} d x = \frac{π}{4} + A,$ then $A$ is equal to

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Correct option is D

∫0π/4 xsin⁡xcos3⁡xdx=∫0π/4 xtan⁡xsec2⁡xdx=xtan2⁡x20π/4−12∫0π/4 tan2⁡xdx=12⋅π4−12∫0π/4 sec2⁡x−1dx=12⋅π4−12[tan⁡x−x]π/4=12⋅π4−121−π4=π4−12

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If ∫0π/4 xsin⁡xcos3⁡xdx=π4+A,then A is equal to

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If $\int_{0}^{π / 4} \frac{x \sin x}{\cos^{3} x} d x = \frac{π}{4} + A,$ then $A$ is equal to