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

int(5x3 + (2x)-1 + e2x )dx

=int(5x3)dx + int((2x)-1)dx + int(e2x )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(e2x)dx = (1/2)e2x + f              where f is another constant of integration

Let C = c+d+f

int((5x3) + (2x-1) + (e2x))dx = (5/4)x4 + (1/2)ln(2x) + (1/2)e2x + C

Answered by Danny L. Maths tutor

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