Question

What is $\int a^x{e}^{x}dx$ equal to?

• A. $\frac{a^x{e}^x}{\ln a}+c$ where $c$ is the constant of integration
• B. $a^x{e}^x+c$ where $c$ is the constant of integration
• C. $\frac{a^x{e}^x}{\ln \left(ae\right)}+c$ where $c$ is the constant of integration
• D. None of the above

Answer 1

Answer: (C)

$\frac{a^x{e}^x}{\ln \left(ae\right)}+c$ where $c$ is the constant of integration

$\int a^x{e}^{x}dx=\int {\left(ae\right)}^{x}dx=\frac{{\left(ae\right)}^x}{\ln \left(ae\right)}+c$
Hence, C is correct.