Evaluate the Integral $$\int e ^ { 2 x } \cos 7 x d x$$

question 129

Multiple Choice

Evaluate the integral.
- $$\int e ^ { 2 x } \cos 7 x d x$$

• A) \(\frac { e ^ { 2 x } } { 2 } [ \sin 7 x + \cos 7 x ] + C\)
• B) \(\frac { e ^ { 2 x } } { 53 } [ 7 \sin 7 x - 2 \cos 7 x ] + C\)
• C) \(\frac { e ^ { 2 x } } { 53 } [ 7 \sin 7 x + 2 \cos 7 x ] + C\)
• D) \(\frac { 1 } { 53 } \left[ 7 e ^ { 2 x } \sin 7 x + 2 \cos 7 x \right] + C\)

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Definitions:

Uric Acid

A waste product found in the blood, created by the breakdown of purines, which are substances found in certain foods and drinks.

Marine Environment

Aquatic habitats that are saline, encompassing oceans, seas, and coastal areas, and host to a diverse range of life forms.

Salt Excretion

The process by which organisms remove excess salt from their bodies, essential for maintaining homeostasis and osmotic balance.

Nitrogenous Wastes

are byproducts of protein and nucleic acid metabolism that organisms must excrete, including urea, ammonia, and uric acid.