E^(4*x-8) include +C

Question

Antiderivatives E^(4*x-8) include +C

Answer 1

Let u = 4x-8

 

Then du = 4dx, so dx = (1/4)du

 

Therefore, ∫e^4x-8dx = ∫e^u(¼)du

 

                               = ¼∫e^udu

 

                               = ¼e^u+C = ¼e^4x-8+C

 

 

Answer 2

to complete this integral, use u substitution.

u=4x-8

du=4

 

Now we have:

∫(e^u)

 

Solve:

(1/4)e^4x-8+C