Find the Integral $\int \cos ^{5} x \sin ^{2} x d x$

question 86

Multiple Choice

Find the integral. $\int \cos ^{5} x \sin ^{2} x d x$

• A) \(\frac{1}{5} \sin ^{5} x-\frac{2}{3} \sin ^{3} x+\sin ^{3} x+C\)
• B) \(\frac{1}{7} \sin ^{7} x-\frac{2}{5} \sin ^{5} x+\frac{1}{3} \sin ^{3} x+C\)
• C) \(\frac{1}{5} \sin ^{5} x+\frac{2}{3} \sin ^{3} x-\sin ^{3} x+C\)
• D) \(\frac{1}{7} \sin ^{7} x+\frac{2}{5} \sin ^{3} x-\frac{1}{3} \sin ^{3} x+C\)

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Definitions:

Minute Flow Rate

The rate at which a fluid flows through a system, measured in units per minute.

Hypernatremia

A medical condition characterized by high concentration of sodium in the blood.

Serum Sodium Concentration

The amount of sodium present in the serum portion of the blood, important for maintaining fluid balance and nerve and muscle function.

Urine Output

The volume of urine expelled from the body over a specified period, which is an important indicator of kidney and overall health.