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Question

Mathematics Question on integral

The value of the integral
∫ex(x2+1)(x+1)2 dx=\int\frac{e^x(x^2+1)}{(x+1)^2}\ dx=

A

exlog⁡(x−1x+1)+ce^x\log(\frac{x-1}{x+1})+c

B

exlog⁡(x+1x−1)+ce^x\log(\frac{x+1}{x-1})+c

C

ex(x+1x−1)+ce^x(\frac{x+1}{x-1})+c

D

ex(x−1x+1)+ce^x(\frac{x-1}{x+1})+c

Answer

ex(x−1x+1)+ce^x(\frac{x-1}{x+1})+c

Explanation

Solution

The correct option is (D) : ex(x−1x+1)+ce^x(\frac{x-1}{x+1})+c.