Use a Table of Integrals with Forms Involving the Trigonometric $\int \frac { 1 } { 1 + e ^ { 5 x } } d x$

question 115

Multiple Choice

Use a table of integrals with forms involving the trigonometric functions to find the integral. $\int \frac { 1 } { 1 + e ^ { 5 x } } d x$

• A) \(\int \frac { 1 } { 1 + e ^ { 5 x } } d x = x ^ { 2 } - \frac { 1 } { 5 } \log \left( e ^ { 5 x } + 1 \right) + C\)
• B) \(\int \frac { 1 } { 1 + e ^ { 5 x } } d x = x - \log \left( e ^ { 5 x } + 1 \right) + C\)
• C) \(\int \frac { 1 } { 1 + e ^ { 5 x } } d x = \log \left( e ^ { 5 x } + 1 \right) + C\)
• D) \(\int \frac { 1 } { 1 + e ^ { 5 x } } d x = x - \frac { 1 } { 5 } \log \left( e ^ { 5 x } + 1 \right) + C\)
• E) \(\int \frac { 1 } { 1 + e ^ { 5 x } } d x = \frac { 1 } { 5 } \log \left( e ^ { 5 x } + 1 \right) + C\)

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