Calculus • Step-by-Step

Integral of sin(2x) dx with Steps

Step-by-step integration of sin(2x) using u-substitution. Shows letting u = 2x to get -(1/2)cos(2x) + C.

Problem Statement

\int \sin(2x) \, dx

Final Result

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

Formula Required: Sine Substitution Rule

The integral of sin(u) is -cos(u) divided by the inner coefficient k.

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

2 Steps

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

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

Apply the Sine Integration to find the antiderivative.

F(x) = -\frac{\mathrm{cos}\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 sin(2x) is -(1/2)cos(2x) + C.