What is the integral of sin(3x)-cos(3x) ?

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

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integral of sin(3x)-cos(3x)

\int sin (3 x) - cos (3 x) d x

- \frac{1}{3} cos (3 x) - \frac{1}{3} sin (3 x) + C

Solution steps

\int sin (3 x) - cos (3 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (3 x) d x - \int cos (3 x) d x

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

\int cos (3 x) d x = \frac{1}{3} sin (3 x)

= - \frac{1}{3} cos (3 x) - \frac{1}{3} sin (3 x)

Add a constant to the solution

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

y^{^{''}} + 4 y^{^{'}} + 5 y = 10

\frac{d}{d x} (3 x^{2} + 2 e^{x})

h (x) = sec (- 4 x^{2} - 3 x + 2)

f (x) = 3 sin (2 x), at x = \frac{π}{8}

x \frac{d y}{d x} = 5 x e^{x} - y + 9 x^{2}

What is the integral of sin(3x)-cos(3x) ?
The integral of sin(3x)-cos(3x) is -1/3 cos(3x)-1/3 sin(3x)+C