Question

$\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 $

Answer 1

Answer: (B)

Let I $\int xe^{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 $