$\text { Evaluate the definite integral } \int \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x \text {. }$
A) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = 5$
B) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = \ln ( 3 )$
C) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = 2$
D) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = \ln ( 4 )$
E) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = \ln ( 1 )$

Question

$\text { Evaluate the definite integral } \int \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x \text {. }$ 
A) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = 5$
B) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = \ln ( 3 )$
C) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = 2$
D) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = \ln ( 4 )$
E) $\int _ { 0 } ^ { 2 } \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x = \ln ( 1 )$

Quizplus · Accepted Answer

To solve the integral $\int \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x$, one would typically complete the square for the quadratic in the denominator or use partial fraction decomposition. However, without going through the detailed steps of solving the integral, the correct answer is determined by evaluating the integral within the given limits, which requires knowledge of calculus techniques. The specific value of $\ln(3)$ suggests that after solving the integral and applying the limits, the result is a logarithmic expression, which is a common outcome for integrals involving rational functions.

Evaluate the definite integral ∫34x2+5x+1dx. \text { Evaluate the definite integral } \int \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x \text {. } Evaluate the definite integral ∫4x2+5x+13​dx.

$\text { Evaluate the definite integral } \int \frac { 3 } { 4 x ^ { 2 } + 5 x + 1 } d x \text {. }$