\( \displaystyle \int e^x\,dx = e^x + C \).

So \( \displaystyle \int_0^{\ln 2} e^x\,dx = [e^x]_0^{\ln 2} = e^{\ln 2} - e^0 = 2 - 1 = 1 \).

Answer: 1.

\( \displaystyle \int e^x\,dx = e^x + C \).

\( \displaystyle \int_0^{2\ln 3} e^x\,dx = [e^x]_0^{2\ln 3} = e^{2\ln 3} - e^0 = 3^2 - 1 = 9 - 1 = 8 \).

Answer: 8.

\( \displaystyle \int_{\ln 2}^{\ln 3} e^x\,dx = [e^x]_{\ln 2}^{\ln 3} = e^{\ln 3} - e^{\ln 2} = 3 - 2 = 1 \).

Answer: 1.

\( \displaystyle \int 4e^{4x}\,dx = e^{4x} + C \).

So \( \displaystyle \int_0^{\ln 3} 4e^{4x}\,dx = [e^{4x}]_0^{\ln 3} = e^{4\ln 3} - e^0 = 3^4 - 1 = 81 - 1 = 80 \).

Answer: 80.

\( \displaystyle \int 2e^{2x}\,dx = e^{2x} + C \).

So \( \displaystyle \int_0^{\ln 4} 2e^{2x}\,dx = [e^{2x}]_0^{\ln 4} = e^{2\ln 4} - e^0 = 4^2 - 1 = 16 - 1 = 15 \).

Answer: 15.