Evaluate the Integral by Making a Substitution and Then Using $$\int \frac { e ^ { 2 x } } { 2 e ^ { x } + 3 } d x$$

question 371

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- $$\int \frac { e ^ { 2 x } } { 2 e ^ { x } + 3 } d x$$

• A) \(\frac { e ^ { x } } { 2 } + \frac { 3 } { 4 } \sin ^ { - 1 } \left| 2 e ^ { x } + 3 \right| + C\)
• B) \(\frac { 3 } { 2 e ^ { x } + 3 } + \ln \left| 2 e ^ { x } + 3 \right| + C\)
• C) \(\frac { e ^ { x } } { 2 } - \frac { 3 } { 4 } \ln \left| 2 e ^ { x } + 3 \right| + C\)
• D) \(\frac { x } { 2 } - \frac { 3 } { 4 } \ln | 2 x + 3 | + C\)

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Definitions:

Nephron

The functional unit of the kidney responsible for filtering blood and producing urine.

Reabsorb

The process by which substances are taken back into the body or tissue after having been secreted or excreted.

Urea

A waste product formed in the liver from the breakdown of proteins and excreted in urine.

Creatinine

A waste product produced by muscles from the breakdown of a compound called creatine, commonly measured to assess kidney function.