Calculus • Step-by-Step

Integral of cos(2x) dx with Steps

Step-by-step integration of cos(2x) dx using u-substitution. Shows letting u = 2x and du = 2 dx to reach (1/2)sin(2x) + C with clear explanations.

Problem Statement

\int \cos(2x) \, dx

Final Result

F(x) = \frac{\mathrm{sin}\left(2 \cdot x\right)}{2} + C

Formula Required: Linear Argument Integration

Integrate cosine to sine and divide by the internal coefficient k.

\int \cos(kx) \, dx = \frac{1}{k}\sin(kx) + C

2 Steps

Set up the indefinite integral with respect to variable $x$.

\int \left( \mathrm{cos}\left(2 \cdot x\right) \right) \, dx

Apply the Cosine Integration to find the antiderivative.

F(x) = \frac{\mathrm{sin}\left(2 \cdot x\right)}{2}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

The integral of cos(2x) is (1/2)sin(2x) + C.