Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ex (ex − 4)(e2x + 1) dx

(1/17) [In |eˣ - 4| - 0.5 In |e²ˣ + 1| - 4 arctan eˣ] + c

Step-by-step explanation:

The solution to the question is provided in the attached image.

The right substitution is y = eˣ

y = eˣ

(dy/dx) = eˣ

dy = eˣ dx

dx = (dy/eˣ)

And x = In y

We then obtain an expression that can be resolved into integrable form by resolving into partial fractions.

After this, the partial fractions is then integrated; giving the final answer obtained.

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0