Find the indefinite integral. $\int \frac { x ^ { 2 } + 18 x + 2 } { x ^ { 3 } + 27 x ^ { 2 } + 6 x } d x$
A) $\frac { 1 } { 3 } \ln \left| x ^ { 3 } + 27 x ^ { 2 } + 6 x \right| + C$
B) $- \frac { 1 } { 3 } \ln \left| x ^ { 3 } + 27 x ^ { 2 } + 6 x \right| + C$
C) $\ln \left| x ^ { 3 } + 27 x ^ { 2 } + 6 x \right| + C$
D) $- 3 \ln \left| x ^ { 3 } + 27 x ^ { 2 } + 6 x \right| + C$
E) $- \ln \left| x ^ { 3 } + 27 x ^ { 2 } + 6 x \right| + C$

Question

Quizplus · Accepted Answer

The integral $\int \frac { x ^ { 2 } + 18 x + 2 } { x ^ { 3 } + 27 x ^ { 2 } + 6 x } d x$ simplifies to $\int \frac {d(x^3 + 27x^2 + 6x)}{3(x^3 + 27x^2 + 6x)}$, which results in $\frac{1}{3}\ln |x^3 + 27x^2 + 6x| + C$.

Find the Indefinite Integral ∫x2+18x+2x3+27x2+6xdx\int \frac { x ^ { 2 } + 18 x + 2 } { x ^ { 3 } + 27 x ^ { 2 } + 6 x } d x∫x3+27x2+6xx2+18x+2​dx

Find the Indefinite Integral $\int \frac { x ^ { 2 } + 18 x + 2 } { x ^ { 3 } + 27 x ^ { 2 } + 6 x } d x$