Question

Evaluate the definite integral of (eᶻ + 1)/(eᶻ + z).

Answer 1

To evaluate the definite integral of (eᶻ + 1)/(eᶻ + z), you can use the substitution method. Let u = eᶻ + z and then perform the integral. The result is ln|eᶻ + z| + C.

Step-by-step explanation:

To evaluate the definite integral of (eᶻ + 1)/(eᶻ + z), we can use the substitution method. Let u = eᶻ + z. Then, du = eᶻ dz. Rearranging the equation, we have dz = du/eᶻ. Substituting these values into the integral, we get:

∫ (eᶻ + 1)/(eᶻ + z) dz = ∫ (eᶻ + 1)/u * du/eᶻ = ∫ du/u = ln|u| + C

Finally, substitute back the value of u we found, we get the final result:

ln|eᶻ + z| + C