Evaluate the Integral $$\int \frac { 4 e ^ { 2 t } - 7 e ^ { t } } { e ^ { 3 t } - 3 e ^ { 2 t } + e ^ { t } - 3 } d t$$

question 35

Multiple Choice

Evaluate the integral.
- $$\int \frac { 4 e ^ { 2 t } - 7 e ^ { t } } { e ^ { 3 t } - 3 e ^ { 2 t } + e ^ { t } - 3 } d t$$

• A) \(\frac { 1 } { 2 } \ln | t - 3 | - \frac { 1 } { 4 } \ln | t + 1 | + \frac { 5 } { 2 } \tan ^ { - 1 } t + C\)
• B) \(\frac { 1 } { 2 } \ln \left| e ^ { t } - 3 \right| - \frac { 1 } { 4 } \ln \left| e ^ { 2 t } + 1 \right| + \frac { 5 } { 2 } \tan ^ { - 1 } \left( e ^ { t } \right) + C\)
• C) \(\frac { 1 } { 4 } \ln \left| e ^ { t } - 3 \right| + \frac { 1 } { 2 } \ln \left| e ^ { 2 t } + 1 \right| + \frac { 3 } { 2 } \tan ^ { - 1 } \left( e ^ { t } \right) + C\)
• D) \(\frac { 1 } { 2 } \ln \left| \mathrm { e } ^ { \mathrm { t } } - 3 \right| - \frac { 1 } { 4 } \ln \left| \mathrm { e } ^ { 2 \mathrm { t } } + 1 \right| + \mathrm { C }\)

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