Q. $\int_{}^{}{xe^{x^{2}}dx}$ is equal to
A) $- \frac{e^{x^{2}}}{2} + c$
B) $\frac{e^{x^{2}}}{2} + c$
C) $\frac{e^{x}}{2} + c$
D) $- \frac{e^{x}}{2} + c$
Explanation
(b)
Let $I = \int_{}^{}{x{\ e}^{x^{2}}dx}$
Put $x^{2} = t\ \Rightarrow 2x\ dx = dt\ \Rightarrow x\ dx = \frac{dt}{2}$
$\therefore I = \frac{1}{2}\int_{}^{}{e^{t}dt = \frac{e^{t}}{2} + c = \frac{e^{x^{2}}}{2} + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.