64. $\int\left(x^{5}+3 e^{x}\right) d x$

Translation:

64. $\int\left(x^{5}+3 e^{x}\right) d x$
Solution. $\int\left(x^{5}+3 e^{x}\right) d x=\int x^{5} d x+3 \int e^{x} d x=\frac{1}{6} x^{6}+3 e^{x}+C$.

Here, properties 3 and 2 (decomposition into a sum of integrals and taking a constant factor outside the integral sign) were applied, and then for the first integral formula 1, for the second - formula III.

Verification: $d\left(\frac{1}{6} x^{6}+3 e^{x}+C\right)=\left(x^{5}+3 e^{x}\right) d x$.