Question

Evaluate \[\int a^x\,dx\]

Options

• \[a^x+\mathrm{C}\]

• \[\frac{a^x}{\log a}+\mathrm{C}\]

• \[\frac{x^{a+1}}{a+1}+\mathrm{C}\]

• \[\log|a^x|+\mathrm{C}\]

Answer 1

The derivative of \(\frac{a^x}{\log a}\) is \(a^x\). Thus, \(\int a^x\,dx=\frac{a^x}{\log a}+\mathrm{C}\).