Provide an appropriate response.
-If we use $u=x^{2}$ as a substitution to find $x e^{x^{2}} d x$, then which of the following would be the correct results?
i. $\int\left(\frac{e^{u}}{2}\right) d u \quad$ ii) $\int\left(2 e^{u}\right) d u \quad$ iii) $\int\left(u e^{u}\right) d u$
A) i is correct.
B) iii is correct.
C) ii is correct.
D) None of these is correct.

Question

Quizplus · Accepted Answer

Using the substitution $u = x^2$, we have $du = 2x \, dx$, so $x \, dx = \frac{1}{2} \, du$. Thus, the integral becomes $\int x e^{x^2} \, dx = \int \frac{1}{2} e^u \, du$.

Provide an Appropriate Response u=x2u=x^{2}u=x2 As a Substitution to Find xex2dxx e^{x^{2}} d xxex2dx

Provide an Appropriate Response $u=x^{2}$ As a Substitution to Find $x e^{x^{2}} d x$