Find the Integral $$\int x ^ { 5 } \ln x d x$$

question 67

Multiple Choice

Find the integral.
$$\int x ^ { 5 } \ln x d x$$

• A) \(\frac { 1 } { 6 } x ^ { 6 } ( 6 \ln x - 1 ) + C\)
• B) \(\frac { 1 } { 36 } x ^ { 6 } ( \ln x - 1 ) + C\)
• C) \(\frac { 1 } { 6 } x ^ { 5 } + \frac { 1 } { x } + C\)
• D) \(\frac { 1 } { 36 } x ^ { 6 } ( 6 \ln x - 1 ) + C\)

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Definitions:

Sample Proportion

The fraction of the sample that represents a particular outcome or characteristic.

Confidence Interval

A range of values derived from sample statistics that is likely to contain the value of an unknown population parameter.

Sample Variance

A measure of the dispersion or spread of data points in a sample, calculated by taking the average of the squared differences from the mean.

Central Limit Theorem

A statistical theory stating that the distribution of sample means will approximate a normal distribution as the sample size becomes large, regardless of the population's distribution.