Question

$\int_{}^{}\frac{2^{x} + 3^{x}}{5^{x}}$dx is equal to –

• A. $\frac{(2/5)^{x}}{\log_{3}(3/5)} + \frac{(3/5)^{x}}{\log_{3}(2/5)}$ + C
• B. $\frac{(2/5)^{x}}{\log_{3}(2/5)} + \frac{(3/5)^{x}}{\log_{3}(3/5)}$ + C
• C. $\frac{(3/5)^{x}}{\log_{3}(2/5)} + \frac{(2/5)^{x}}{\log_{3}(3/5)}$ + C
• D. None of the above

Answer 1

Answer: (B)

$\frac{(2/5)^{x}}{\log_{3}(2/5)} + \frac{(3/5)^{x}}{\log_{3}(3/5)}$ + C

Answer 2

$\int \left( \frac { 2 } { 5 } \right) ^ { x } + \left( \frac { 3 } { 5 } \right) ^ { x }$ dx = $\frac { ( 2 / 5 ) ^ { x } } { \log ( 2 / 5 ) } + \frac { ( 3 / 5 ) ^ { x } } { \log ( 3 / 5 ) }$ + C