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Question

ex54ex+e2xdx

A
cos1(ex+23)+c
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B
cos1(ex32)+c
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C
sin1(ex+23)+c
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D
sin1(ex32)+c
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Solution

The correct option is A cos1(ex+23)+c
ex54ex+e2xdx

Putting ex=t

exdx=dt

=dt54t+t2

dt(t24t+4)+1

=dt(t2)2+1

=ln(t2)+(t2)2+1+c

=ln(ex2)+e2x4ex+5+c

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