Evaluate the Integral Using the Indicated Trigonometric Substitution $\int \frac{x^{3}}{\sqrt{x^{2}+16}} d x ; x=4 \tan \theta$

question 45

Multiple Choice

Evaluate the integral using the indicated trigonometric substitution. $\int \frac{x^{3}}{\sqrt{x^{2}+16}} d x ; x=4 \tan \theta$

• A) \(\frac{3}{2}(x+16)^{3 / 2}-16 \sqrt{x+16}+C\)
• B) \(\left(x^{2}+16\right)^{3 / 2}-\sqrt{x^{2}+16}+C\)
• C) \(\frac{1}{3}\left(x^{2}+16\right)^{3 / 2}-\sqrt{x^{2}+16}+C\)
• D) \(\frac{1}{3}\left(x^{2}+16\right)^{3 / 2}+16 \sqrt{x^{2}+16}+C\)
• E) \(\left(x^{2}+16\right)^{3 / 2}-4 \sqrt{x^{2}+16}+C\)

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Bootstrap

A statistical method that involves resampling a single dataset to create many simulated samples, used in assessing variability.

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