Find the indefinite integral. $\int 2 x e ^ { 4 x ^ { 2 } } d x$
A) $16 x ^ { 2 } e ^ { 4 x ^ { 2 } } + C$
B) $\frac { 1 } { 4 } x e ^ { 4 x ^ { 2 } } + C$
C) $\frac { 1 } { 4 } e ^ { 4 x ^ { 2 } } + C$
D) $\frac { 1 } { 2 } e ^ { 4 x ^ { 2 } } + C$
E) $8 x e ^ { 4 x ^ { 2 } } + C$

Question

Quizplus · Accepted Answer

To solve the integral $\int 2 x e ^ { 4 x ^ { 2 } } d x$, we can use a substitution method. Let $u = 4x^2$, then $du = 8x dx$. However, we need to adjust for the factor of 2 in the integral, so we consider $du/4 = 2x dx$. Substituting these into the integral gives $\int e^u \frac{du}{4}$, which simplifies to $\frac{1}{4} e^u + C$. Reverting back to the original variable, we get $\frac{1}{4} e^{4x^2} + C$.

Find the Indefinite Integral ∫2xe4x2dx\int 2 x e ^ { 4 x ^ { 2 } } d x∫2xe4x2dx

Find the Indefinite Integral $\int 2 x e ^ { 4 x ^ { 2 } } d x$