$\text { Use integration tables to find } \int \frac { 1 } { 5 x ^ { 2 } + 3 x + 3 } d x \text {. }$

question 10

Multiple Choice

$\text { Use integration tables to find } \int \frac { 1 } { 5 x ^ { 2 } + 3 x + 3 } d x \text {. }$

• A) \(\frac { 2 } { \sqrt { 51 } } \arctan \left( \frac { 10 x + 3 } { \sqrt { 51 } } \right) + C\)
• B) \(\quad \frac { 1 } { \sqrt { 51 } } \ln \left| \frac { 10 x + 3 - \sqrt { 51 } } { 10 x + 3 + \sqrt { 51 } } \right| + C\)
• C) \(\frac { 1 } { 10 } \left( \ln \left| 3 + 3 x + 5 x ^ { 2 } \right| - \frac { 6 } { \sqrt { 51 } } \arctan \left( \frac { 10 x + 3 } { \sqrt { 51 } } \right) \right) + C\)
• D) \(\frac { 1 } { \sqrt { 51 } } \ln \left| \frac { 10 x - 3 + \sqrt { 51 } } { 10 x + 3 + \sqrt { 51 } } \right| + C\)
• E) \(\frac { 2 } { \sqrt { 51 } } \arctan \left( \frac { 10 x - 3 } { \sqrt { 51 } } \right) + C\)

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Definitions:

Variable Substitution

In mathematics, this involves replacing variables with other variables or values to simplify expressions or solve equations.

Mathematical Expression

A combination of numbers, operations, and sometimes variables that represents a mathematical relationship or value.

Exponentiation

The mathematical operation involving the raising of a number to the power of another number.

Mathematical Expression

A combination of numbers, operations, and symbols forming a meaningful equation or inequality.