67. $\int\left(x^{3}+2^{x}\right) d x$
Solution. $\int\left(x^{3}+2^{x}\right) d x=\int x^{3} d x+\int 2^{x} d x=\frac{1}{4} x^{4}+\frac{2^{x}}{\ln 2}+C$. Since differentiating the result yields the integrand, the solution is correct.