Use Integration by Parts to Evaluate the Integral $\int \frac { x } { \sqrt { x + 16 } } d x$

question 17

Multiple Choice

Use integration by parts to evaluate the integral $\int \frac { x } { \sqrt { x + 16 } } d x$ .

• A) \(\frac { 2 } { 3 } ( x + 16 ) ^ { 3 / 2 } ( x - 32 ) + C\)
• B) \(\frac { 2 } { 3 } ( x - 16 ) ^ { 1 / 2 } ( x + 32 ) + C\)
• C) \(\frac { 2 } { 3 } ( x + 16 ) ^ { 1 / 2 } ( x - 32 ) + C\)
• D) \(\frac { 3 } { 2 } ( x + 16 ) ^ { 1 / 2 } ( x - 32 ) + C\)

---

Definitions:

Precipitation

Any type of water, whether in liquid or solid state, that descends from the sky and makes contact with the Earth's surface, encompassing phenomena such as rain, snow, sleet, and hail.

Vegetation

Plant life or the lifeforms characteristic of a region, period, or special environment, playing key roles in the Earth's ecosystem.

Sea Level

The average height of the ocean's surface between high and low tide, used as a reference point in measuring land elevation and sea depth.

Earth's Tilt

The angle between Earth's rotational axis and its orbital plane around the sun, influencing seasonal variations.