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Q.

∫etanxsinx−secxdx=

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a

etanx.cosx+C

b

etanx.sinx+C

c

−etanx.cosx+C

d

etanx.secx+C

answer is C.

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Detailed Solution

∫etansin⁡xdx−∫etan⁡xsec⁡xdx  (by parts) =−cos⁡xetan⁡x+∫cos⁡xetan⁡x⋅sec2⁡xdx−∫etan⁡xsec⁡xdx=−cos⁡x⋅etan⁡x+C
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