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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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