Answer to Question #132617 in Calculus for qwerty

Question

\int \left(e^x+2^x\right)dx

Answer 1

$\int(e^x+2^x)dx=\int(e^x+(e^{ln(2)})^x)dx=\\ \int(e^x+e^{x\cdot ln(2)})dx=\int e^xdx+\int e^{x\cdot ln(2)}dx=\\ e^x+\frac{1}{ln(2)}\int e^{x\cdot ln(2)}d(x\cdot ln(2))=\\ e^x+\frac{1}{ln(2)}\cdot e^{x\cdot ln(2)}+C=\\ e^x+\frac{1}{ln(2)}\cdot(e^{ln(2)})^x+C=\\ e^x+\frac{2^x}{ln(2)}+C.$

Answer: $e^x+\frac{2^x}{ln(2)}+C.$