Verify the Integration Formula

question 147

True/False

Verify the integration formula.
- $$\int 2 x ^ { 3 } \operatorname { sech } ^ { - 1 } x ^ { 2 } d x = \frac { x ^ { 4 } } { 2 } \operatorname { sech } ^ { - 1 } x + \frac { 1 } { 2 } \sqrt { 1 - x ^ { 4 } } + C$$

---

Definitions:

Kava

A beverage made from the roots of the kava plant, traditionally consumed in the Pacific Islands, known for its sedative and anxiolytic effects.

Calmative

An agent or approach that has a calming effect, reducing excitement or anxiety.

Designer Drugs

Synthetic substances created to mimic the effects of illegal drugs, often with modified chemical structures to evade law enforcement detection.

Physical Dependence

A physiological state where the body adapts to a substance, leading to withdrawal symptoms when that substance is reduced or stopped.