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$\int \sec^{4} x {cosec}^{2} x d x, is equal to$

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3tan3x+2tanx−tanx+C

13tan3x+tanx−cotx+C

13tan3x+2tanx−cotx+C

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detailed solution

Correct option is C

We have I=∫sec4⁡xcosec2⁡xdx=∫1+tan2⁡xsec2⁡x1+cot2⁡xdx =∫1+t21+1t2dt[ putting tan⁡x=t] =∫t2+2+1t2dt=13t3+2t−1t+C =13tan3⁡x+2tan⁡x−cot⁡x+C

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∫sec4⁡xcosec2⁡xdx , is equal to

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$\int \sec^{4} x {cosec}^{2} x d x, is equal to$