Question

$\int x{e}^{x^2}dx$ 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 $\int x{e}^{x^2}dx$

Put$x^2=t\Rightarrow 2xdx=dt\Rightarrow xdx=\frac{dt}{2}$

$\therefore I=\frac{1}{2}\int e^{t}dt=\frac{e^t}{2}+C=\frac{e^{x^2}}{2}+C$