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Question

esin1x[1+x1x2] dx =

A
xesin1x+c
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B
esin1x+c
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C
11x2esin1x+c
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D
x2esin1X+c
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Solution

The correct option is A xesin1x+c
I=esin1x[1+x1x2]dx
Put sin1x=t
x=sint
dx=costdt
So, I=et(sint+cost)dt
I=(sint+cost)et(costsint)etdt
I=(sint+cost)et(costsint)etet(sint+cost)dt
2I=2sintet+C
I=xesin1x+C

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