What is the integral of sin(x)-6cos(x) ?

The integral of sin(x)-6cos(x) is -cos(x)-6sin(x)+C

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integral of sin(x)-6cos(x)

\int sin (x) - 6 cos (x) d x

- cos (x) - 6 sin (x) + C

Solution steps

\int sin (x) - 6 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 6 cos (x) d x

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

\int 6 cos (x) d x = 6 sin (x)

= - cos (x) - 6 sin (x)

Add a constant to the solution

= - cos (x) - 6 sin (x) + C

\int (\frac{1}{x ^{2} + 2 x}) d x

\int 4 x^{2} (4 x - 5)^{2} d x

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

sin (π x)

\int \frac{9 x ^{2} - 9}{x ^{3}} d x

What is the integral of sin(x)-6cos(x) ?
The integral of sin(x)-6cos(x) is -cos(x)-6sin(x)+C