Find the Integral Using an Appropriate Trigonometric Substitution $\int \frac{x^{3}}{\sqrt{x^{2}+36}} d x$

question 117

Multiple Choice

Find the integral using an appropriate trigonometric substitution. $\int \frac{x^{3}}{\sqrt{x^{2}+36}} d x$

• A) \(\frac{1}{3}\left(x^{2}-36\right)^{3 / 2} \sqrt{x^{2}+36}+C\)
• B) \(\frac{1}{3}\left(x^{2}+72\right) \sqrt{x^{2}+36}+C\)
• C) \(\frac{1}{3}\left(x^{2}-72\right) \sqrt{x^{2}+36}+C\)
• D) \(\frac{1}{3}\left(x^{2}+36\right)^{3 / 2} \sqrt{x^{2}+36}+C\)

---

Definitions:

Gross Pay

The total amount of money earned by an employee before any deductions or taxes are taken out.

Deductions

Amounts subtracted from gross income to determine taxable income, including expenses, exemptions, and allowances.

Long-Term Liabilities

Financial obligations of a business that are due more than one year in the future.

Current Liabilities

Debts or obligations that are due to be paid within one year or within the normal operating cycle.