Evaluate the Integral by Using a Substitution Prior to Integration $\int \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + 21 } } d x$

question 89

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $\int \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + 21 } } d x$

• A) \(\frac { 3 x } { 2 } \sqrt { x ^ { 2 } + 21 } - \frac { 21 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 21 } \right) + C\)
• B) \(\frac { 3 x } { 2 } \sqrt { x ^ { 2 } + 21 } + \frac { 21 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 21 } \right) + C\)
• C) \(\frac { x } { 2 } \sqrt { x ^ { 2 } + 21 } + \frac { 21 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 21 } \right) + C\)
• D) \(\frac { x } { 2 } \sqrt { x ^ { 2 } + 21 } - \frac { 21 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 21 } \right) + C\)

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Definitions:

Contraries

Statements or propositions that cannot both be true at the same time, but can both be false.

Contradictories

Statements that cannot both be true at the same time and under the same circumstances.

Contraries

Statements, concepts, or propositions that cannot both be true at the same time, but can both be false.

Subcontraries

In traditional logic, propositions that cannot both be false but can both be true, specific within the square of opposition.