Evaluate the Integral by Making a Substitution and Then Using $$\int e ^ { x } \sqrt { 25 - e ^ { 2 x } } d x$$

question 95

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- $$\int e ^ { x } \sqrt { 25 - e ^ { 2 x } } d x$$

• A) \(\frac { \mathrm { e } ^ { \mathrm { x } } } { 2 } \sqrt { 25 - \mathrm { e } ^ { 2 \mathrm { x } } } + \frac { 25 } { 2 } \sin ^ { - 1 } \left( \frac { \mathrm { e } ^ { \mathrm { x } } } { 5 } \right) + \mathrm { C }\)
• B) \(\frac { e ^ { x } } { 2 } \sqrt { 25 - e ^ { 2 x } } + \frac { 25 } { 2 } \ln \left| e ^ { x } + \sqrt { e ^ { 2 x } - 25 } \right| + C\)
• C) \(\frac { 25 } { 2 } \sin ^ { - 1 } \left( \frac { e ^ { x } } { 5 } \right) + C\)
• D) \(\frac { \mathrm { e } ^ { \mathrm { x } } } { 2 } \sqrt { 25 - \mathrm { e } ^ { 2 \mathrm { x } } } + \frac { 25 } { 2 } \ln \left| \mathrm { x } + \sqrt { \mathrm { x } ^ { 2 } - 25 } \right| + \mathrm { C }\)

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