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Question

ex[1+sinx1+cosx]dx is equal to
(where c is integration constant)

A
extanx2+c
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B
extanx2+c
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C
ex1+cosx+c
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D
ex[1+sin(x2)]+c
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Solution

The correct option is A extanx2+c
I=ex[1+sinx1+cosx]dx =ex[11+cosx+sinx1+cosx]dx

We know
1+cos2x=2cos2xsin2x=2sinxcosx
So,
I=ex[12sec2(x2)+tan(x2)]dx f(x) f(x) I=extan(x2)+c[ex[f(x)+f(x)] dx=exf(x)+c]

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