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Question

ex[x3+x+1(1+x2)3/2]dx is equal to


A

x2ex(1+x2)1/2+c

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B

exx(1+x2)1/2+c

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C

ex(1+x2)1/2+c

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D

xex(1+x2)1/2+c

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Solution

The correct option is D

xex(1+x2)1/2+c


I=ex[x1+x2+1(1+x2)3/2]dx

Let f(x)=x1+x2f(x)=1+x2x21+x2(1+x2)

=1(1+x2)3/2

I=exf(x)+c

=exx1+x2+c


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