Question

evaluate the integral ∫(2cosx+2e^x+5sinx)dx

Answer 1

The integral of a sum is the sum of the integrals:
∫(Ax+Bx)dx = (∫Ax dx) + (∫Bx dx)

So in this case, ∫(2cosx+2e^x+5sinx)dx = 2∫cosxdx + 2∫e^xdx + 5∫sinxdx = 2sinx + 2e^x - 5cosx + C

C = Integration constant

Those integrals are very simple direct integrals, which you can find in any table like this one:

http://www.hardycalculus.com/calcindex/IE_itbasic.htm

Answer 2

thanks....