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

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

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

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

- cos (x) - 3 sin (x) + C

Solution steps

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

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

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

= - cos (x) - 3 sin (x)

Add a constant to the solution

= - cos (x) - 3 sin (x) + C

\int \frac{3 x ^{2} - 4}{x ^{3} - 4 x} d x

\int \frac{x ^{2} - 4 x + 5}{2 x} d x

\int x e^{x y} cos (2 x) - 3 d y

\int \frac{1}{1 + y + 1} d y

\int x^{2} (x^{3} - 2) d x

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