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Question

ex(1x)2(1+x2)2dx.

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Solution

I=ex(1x)2(1+x2)2dx
I=ex(1+x22x)(1+x2)2dx
I=ex(1+x2(1+x2)22x(1+x2)2)dx
I=ex(11+x22x(1+x2)2)dx ……..(i)
which is of the form ex(f(x)+f(x))dx=ex f(x)+c
where f(x)=11+x2 such that f(x)=(2x)(1+x2)2
I=ex(11+x2)+c.

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