Evaluate the Integral $$\int \mathrm { e } ^ { 3 x } \cos 2 \mathrm { xdx }$$

question 48

Multiple Choice

Evaluate the integral.
- $$\int \mathrm { e } ^ { 3 x } \cos 2 \mathrm { xdx }$$

• A) \(\frac { 1 } { 13 } \left[ 2 \mathrm { e } ^ { 3 \mathrm { x } } \sin 2 \mathrm { x } + 3 \cos 2 \mathrm { x } \right] + \mathrm { C }\)
• B) \(\frac { e ^ { 3 x } } { 13 } [ 2 \sin 2 x - 3 \cos 2 x ] + C\)
• C) \(\frac { e ^ { 3 x } } { 13 } [ 2 \sin 2 x + 3 \cos 2 x ] + C\)
• D) \(\frac { \mathrm { e } ^ { 3 x } } { 2 } [ \sin 2 x + \cos 2 x ] + C\)

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Aquatic Habitat

encompasses ecosystems in water environments, providing living space and necessary resources for aquatic organisms.

Cold Ecosystem

An ecosystem characterized by low temperatures and short growing seasons, often found in polar or high-altitude regions.

Coniferous Forest

A biome characterized by trees with needles or scale-like leaves, including many species that bear cones.