Evaluate the Integral $$\int \frac { 3 e ^ { 4 t } + 12 e ^ { 2 t } + 4 } { e ^ { 2 t } + 4 } d t$$

question 305

Multiple Choice

Evaluate the integral.
- $$\int \frac { 3 e ^ { 4 t } + 12 e ^ { 2 t } + 4 } { e ^ { 2 t } + 4 } d t$$

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

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