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etanx(sinxsecx)dx, is equal to 

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By Expert Faculty of Sri Chaitanya
a
etan⁡x⋅cos⁡x+C
b
etan⁡x⋅sin⁡x+C
c
−etan⁡x⋅cos⁡x+C
d
etan⁡x⋅sec⁡x+C
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detailed solution

Correct option is C

I=∫etan⁡x(sinx-secx)dx=∫sin⁡x⋅etan⁡xdx−∫sec⁡x⋅etan⁡xdx=−etan⁡x⋅cos⁡x+∫cos⁡x⋅etan⁡x⋅sec2⁡xdx−∫sec⁡x⋅etan⁡xdx=−cos⁡x⋅etan⁡x+C


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