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Question

ex1-x21+x22 dx

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Solution

Let I=ex1-x21+x22dx=ex1+x2-2x1+x22dx=ex11+x2-2x1+x22dxHere, f(x)=11+x2f'(x)=-2x1+x22Put exf(x)=tex11+x2=tDiff both sides w.r.t xex11+x2+ex-11+x222x=dtdxex11+x2-2x1+x22dx=dtex11+x2-2x1+x22dx=dtI=t+C=ex1+x2+C

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