MCQMediumJEE Main 2023 · 6 April, Shift 1Integration Techniques (Substitution, Parts, Partial Fractions)

Mathematics Question from JEE Main 2023 · 6 April, Shift 1

Let I(x)=∫x2(xsec⁡2x+tan⁡x)(xtan⁡x+1)2 dxI(x) = \int \frac{x^2(x\sec^2 x + \tan x)}{(x\tan x + 1)^2} \, dx. If I(0)=0I(0) = 0, then I(π4)I\left(\frac{\pi}{4}\right) is equal to:

  • A

    log⁡e((π+4)216)+π24(π+4)\log_e\left(\frac{(\pi+4)^2}{16}\right) + \frac{\pi^2}{4(\pi+4)}

  • B

    log⁡e((π+4)232)−π24(π+4)\log_e\left(\frac{(\pi+4)^2}{32}\right) - \frac{\pi^2}{4(\pi+4)}

  • C

    log⁡e((π+4)216)−π24(π+4)\log_e\left(\frac{(\pi+4)^2}{16}\right) - \frac{\pi^2}{4(\pi+4)}

  • D

    log⁡e((π+4)232)+π24(π+4)\log_e\left(\frac{(\pi+4)^2}{32}\right) + \frac{\pi^2}{4(\pi+4)}

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