Evaluate the Integral Using the Given Substitution $\int \frac { d x } { \sqrt { 6 x + 3 } } , \quad u = 6 x + 3$

question 82

Multiple Choice

Evaluate the integral using the given substitution.
- $\int \frac { d x } { \sqrt { 6 x + 3 } } , \quad u = 6 x + 3$

• A) \(3 \frac { 1 } { \sqrt { 6 x + 3 } } + C\)
• B) \(\frac { 1 } { 6 ( 6 x + 3 ) ^ { 3 / 2 } } + C\)
• C) \(\frac { 1 } { 3 } \sqrt { 6 x + 3 } + C\)
• D) \(2 \sqrt { 6 x + 3 } + C\)

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Definitions:

Electron Transport System

A series of protein complexes located in the mitochondria or chloroplasts that transfer electrons, creating an electrochemical gradient to produce ATP.

ATP

Adenosine triphosphate, a molecule that carries energy within cells for metabolism.

NADPH

Nicotinamide adenine dinucleotide phosphate, a cofactor used in anabolic reactions, such as lipid and nucleic acid synthesis, serving as a reducing agent by donating electrons and hydrogen.

Theodor Engelmann

A 19th-century German biologist and physician known for his work on photosynthesis and the action spectrum of chlorophyll.