Question

State true or false.

$\int a^{x}dx=\frac{a^x}{\log a}+c$

• A. True
• B. False

Answer 1

The correct option is A True

Let $t=a^x$

$\Rightarrow \log t=x\log a$

$\Rightarrow \frac{1}{t}dt=\log adx$

$\Rightarrow dt=t\log adx$

$\Rightarrow dx=\frac{dt}{t\log a}$

$\int a^{x}dx=\int t\frac{dt}{t\log a}$

$=\frac{1}{\log a}\int dt$

$=\frac{1}{\log a}t+c$

$=\frac{1}{\log a}{a}^x+c$

$=\frac{a^x}{\log a}+c$

Hence the given statement is true.