Calculus • Step-by-Step

Integral of sin(3x) dx with Steps

Find the integral of sin(3x) dx step by step. Uses u-substitution with u = 3x to evaluate the trigonometric integral and obtain -(1/3)cos(3x) + C.

Problem Statement

\int \sin(3x) \, dx

Final Result

F(x) = -\frac{\mathrm{cos}\left(3 \cdot x\right)}{3} + C

Formula Required: Trig u-Substitution

Let u = 3x, du = 3 dx. Reversing differentiation divides by 3.

\int \sin(3x) \, dx = -\frac{1}{3}\cos(3x) + C

2 Steps

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

\int \left( \mathrm{sin}\left(3 \cdot x\right) \right) \, dx

Apply the Sine Integration to find the antiderivative.

F(x) = -\frac{\mathrm{cos}\left(3 \cdot x\right)}{3}

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The integral of sin(3x) is -(1/3)cos(3x) + C.