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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

x = y^{2} - 36, x = 36 - y^{2}

\frac{d}{d x} (6 ln (4 x))

\int \frac{8}{x} d x

\frac{d y}{d x} = 85 y x^{16}

\frac{d y}{d t} = - 5 y

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