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The value of $\int_{0}^{π / 2} \frac{d x}{1 + \tan^{3} x}$ is

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π/4

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Correct option is C

I=∫0π/2 dx1+tan3⁡ x=∫0π/2 dx1+tan3⁡ (π/2−x)=∫0π/2 dx1+cot3⁡ x=∫0π/2 tan3⁡ x1+tan3⁡ xdx=∫0π/2 1−11+tan3⁡ xdx=π2−I.Thus I=π/4.

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The value of ∫0π/2 dx1+tan3⁡ x is

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The value of $\int_{0}^{π / 2} \frac{d x}{1 + \tan^{3} x}$ is