## Step-by-step explanation

Problem to solve:

Learn how to solve definite integrals problems step by step online.

$\int_{1}^{3}\frac{1+\cos\left(2x\right)}{2}dx$

Learn how to solve definite integrals problems step by step online. Integrate cos(x)^2 from 1 to 3. Apply the identity: \cos\left(x\right)^2=\frac{1+\cos\left(2x\right)}{2}. Take the constant \frac{1}{2} out of the integral. Expand the integral. The integral of a constant is equal to the constant times the integral's variable.