Find the indefinite integral. $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$
A) $\frac { \ln \left| - 4 x ^ { 2 } + 9 \right| } { - 4 x ^ { 2 } + 9 } + C$
B) $\frac { - 1 } { 8 } \ln \left| - 4 x ^ { 2 } + 9 \right| + C$
C) $\ln \left| - 4 x ^ { 2 } + 9 \right| + C$
D) $\ln \left| - 4 x ^ { 2 } - 9 \right| + C$
E) $\frac { 1 } { - 8 x } + C$

Question

Quizplus · Accepted Answer

This integral can be solved by recognizing it as a derivative of a logarithmic function. The derivative of $\ln|f(x)|$ is $\frac{f'(x)}{f(x)}$, and in this case, $f(x) = -4x^2 + 9$, with $f'(x) = -8x$. Thus, the integral $\int \frac{x}{-4x^2 + 9} dx$ simplifies to $\frac{-1}{8} \ln|-4x^2 + 9| + C$, making choice B correct.

Find the Indefinite Integral ∫x−4x2+9dx\int \frac { x } { - 4 x ^ { 2 } + 9 } d x∫−4x2+9x​dx

Find the Indefinite Integral $\int \frac { x } { - 4 x ^ { 2 } + 9 } d x$