Answer to Question #132618 in Calculus for qwerty

Question

\int 3^x dx

Answer 1

$\int3^xdx=\int(e^{ln(3)})^xdx=\\ \int e^{x\cdot ln(3)}dx=\int e^{x\cdot ln(3)}dx=\\ \frac{1}{ln(3)}\int e^{x\cdot ln(3)}d(x\cdot ln(3))=\\ \frac{1}{ln(3)}\cdot e^{x\cdot ln(3)}+C=\\ \frac{1}{ln(3)}\cdot(e^{ln(3)})^x+C=\\ \frac{3^x}{ln(3)}+C.$

Answer: $\frac{3^x}{ln(3)}+C.$