∫$$0$$π$$/2$$ $$dx2cos$$⁡$$x+3$$ is equal to

Correct option is 125tan−1⁡15

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$\int_{0}^{π / 2} \frac{d x}{2 \cos x + 3}$ is equal to

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detailed solution

Correct option is A

Put tan⁡x/2=t The given integral reduces to ∫01 2dt1+t221−t21+t2+3=2∫01 dt2−2t2+3+3t2=2∫01 dtt2+5 =25tan−1⁡t501=25tan−1⁡15

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∫0π/2 dx2cos⁡x+3 is equal to

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$\int_{0}^{π / 2} \frac{d x}{2 \cos x + 3}$ is equal to