Question

Evaluate $\int 3^x\cdot {\pi }^{x}dx$
(where $C$ is constant of integration)

• A. $\frac{3^x\cdot {\pi }^x}{\ln 3\pi }+C$
• B. $\frac{3^x\cdot {\pi }^x}{\ln \pi }+C$
• C. $-\frac{3^x\cdot {\pi }^x}{\ln 3\pi }+C$
• D. $\frac{3^x\cdot {\pi }^x}{\ln 3}+C$

Answer 1

The correct option is A $\frac{3^x\cdot {\pi }^x}{\ln 3\pi }+C$

Let $I=\int 3^x\cdot {\pi }^{x}dx$
$\Rightarrow I=\int (3\pi {)}^{x}dx=\frac{(3\pi {)}^x}{\ln \left(3\pi \right)}+C$

$\Rightarrow I=\frac{3^x\cdot {\pi }^x}{\ln 3\pi }+C$