Integrate ((5x^3) + ((2x)^-1) + (e^2x))dx.

int(5x³ + (2x)^-1 + e^2x )dx

=int(5x³)dx + int((2x)^-1)dx + int(e^2x )dx

int(5x³)dx = (5/4)x⁴+ c               where c is the constant of integration

int(2x^-1)dx = (1/2)ln(2x) + d       where d is another constant of integration

int(e^2x)dx = (1/2)e^2x + f              where f is another constant of integration

Let C = c+d+f

int((5x³) + (2x^-1) + (e^2x))dx = (5/4)x⁴ + (1/2)ln(2x) + (1/2)e^2x + C