Find an Antiderivative of the Given Function $\frac { 4 } { 5 } \csc ^ { 2 } \frac { x } { 5 }$

question 156

Multiple Choice

Find an antiderivative of the given function.
- $\frac { 4 } { 5 } \csc ^ { 2 } \frac { x } { 5 }$

• A) \(\frac { 4 } { 25 } \cot \frac { x } { 5 }\)
• B) \(\frac { 8 } { 5 } \csc ^ { 2 } \frac { x } { 5 } \cot \frac { x } { 5 }\)
• C) \(4 \cot \frac { x } { 5 }\)
• D) \(- 4 \cot \frac { x } { 5 }\)

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Definitions:

Explosive Reactions

Chemical reactions that occur with a sudden release of energy, often accompanied by the production of heat and light.

Nitro Groups

Functional groups in organic chemistry consisting of one nitrogen atom connected by a double bond to one oxygen atom and by a single bond to another oxygen atom; they are denoted as NO2 and contribute to the reactivity of molecules.

Neutral Oxygen Balance

A term in explosives chemistry indicating that an explosive compound has an oxygen balance of zero, meaning it has exactly enough oxygen to oxidize all its components.

Oxidize

A chemical process involving the transfer of electrons from a substance to an oxidizing agent, increasing the oxidation state of the substance.