Question

$\int_{}^{}{e^{x}\left( \frac{1 - x}{1 + x^{2}} \right)^{2}}$dx =

• A. $\frac{e^{x}}{(1 + x^{2})^{2}}$+ c
• B. $- \frac{e^{x}}{1 + x^{2}}$ + c
• C. $\frac{e^{x}}{1 + x^{2}}$ + c
• D. None of these

Answer 1

Answer: (C)

$\frac{e^{x}}{1 + x^{2}}$ + c

Answer 2

$\int_{}^{}{e^{x}\left( \frac{1 + x^{2} - 2x}{(1 + x^{2})^{2}} \right)dx}$= $I _ { 1 } = \int t ^ { 1 / 2 } d t = \frac { t ^ { 3 / 2 } } { 3 / 2 } + c _ { 1 }$

= e^x . $\frac{1}{1 + x^{2}} + c$