Find an antiderivative of the given function.
-$$- \frac { 30 } { x ^ { 7 } }$$
A) $- \frac { 6 } { x ^ { 5 } }$
B) $\frac { 6 } { x ^ { 6 } }$
C) $\frac { 5 } { x ^ { 7 } }$
D) $\frac { 5 } { x ^ { 6 } }$

Question

Quizplus · Accepted Answer

Using the power rule for antiderivatives, we add 1 to the exponent and divide by the new exponent: 
\begin{align*}
\int -\frac{30}{x^7} dx &= -30\int x^{-7} dx \
&= -30\frac{x^{-6}}{-6} + C \
&= 5x^{-6} + C \
&= \frac{5}{x^6} + C
\end{align*}
Thus, the best choice is (D).

Find an Antiderivative of the Given Function −30x7- \frac { 30 } { x ^ { 7 } }−x730​

Find an Antiderivative of the Given Function $- \frac { 30 } { x ^ { 7 } }$