Evaluate the given integral using the substitution.
$\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x$
A) $- e ^ { - 4 x } + C$
B) $- 4 e ^ { - 4 x } + C$
C) $- \frac { 1 } { 4 } e ^ { - 4 x } + C$
D) $- \frac { 1 } { 4 } e ^ { - 8 x } + C$
E) $- e ^ { - 8 x } + C$

Question

Evaluate the given integral using the substitution.  
  $\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x$  
A) $- e ^ { - 4 x } + C$
B)   $- 4 e ^ { - 4 x } + C$
C)   $- \frac { 1 } { 4 } e ^ { - 4 x } + C$
D)   $- \frac { 1 } { 4 } e ^ { - 8 x } + C$
E)   $- e ^ { - 8 x } + C$

Quizplus · Accepted Answer

Using the substitution $u = -4x$, we have $\mathrm{d}u = -4 \mathrm{d}x$, which implies $\mathrm{d}x = \frac{\mathrm{d}u}{-4}$. Substituting into the integral gives $\int e^u \frac{\mathrm{d}u}{-4}$, which simplifies to $-\frac{1}{4} e^u + C$. Substituting back $u = -4x$, we get $-\frac{1}{4} e^{-4x} + C$.

Evaluate the Given Integral Using the Substitution ∫e−4x dx;u=−4x\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x∫e−4x dx;u=−4x

Evaluate the Given Integral Using the Substitution $\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x$