Use a table of integrals to evaluate the integral.
$\int \frac { \sqrt { 6 x + 5 } } { x ^ { 2 } } d x$
A) $- \frac { \sqrt { 6 x + 5 } } { x } + \frac { 3 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C$
B)
$- \frac { \sqrt { 6 x + 5 } } { x } + \frac { 6 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C$
C)
$- \frac { 6 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C$
D)
$- \frac { 3 \sqrt { 5 } } { 5 } \ln \left| \frac { \sqrt { 6 x + 5 } - \sqrt { 5 } } { \sqrt { 6 x + 5 } + \sqrt { 5 } } \right| + C$

Question

Quizplus · Accepted Answer

The integral involves a substitution that simplifies the expression to a form that can be directly integrated using standard integral formulas. The correct answer includes both a term that results from the direct integration of the transformed expression and a logarithmic term that arises from integrating the derivative of the square root function inside the logarithm, which matches option A.

Use a Table of Integrals to Evaluate the Integral ∫6x+5x2dx\int \frac { \sqrt { 6 x + 5 } } { x ^ { 2 } } d x∫x26x+5​​dx

Use a Table of Integrals to Evaluate the Integral $\int \frac { \sqrt { 6 x + 5 } } { x ^ { 2 } } d x$