What is the integral of sin(x)-12cos(x) ?

The integral of sin(x)-12cos(x) is -cos(x)-12sin(x)+C

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integral of sin(x)-12cos(x)

\int sin (x) - 12 cos (x) d x

- cos (x) - 12 sin (x) + C

Solution steps

\int sin (x) - 12 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 12 cos (x) d x

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

\int 12 cos (x) d x = 12 sin (x)

= - cos (x) - 12 sin (x)

Add a constant to the solution

= - cos (x) - 12 sin (x) + C

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\int \frac{1}{( x ^{2} + \frac{3}{4} ) ^{2}} d x

\int \frac{e ^{2 x}}{e ^{x + 3}} d x

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

What is the integral of sin(x)-12cos(x) ?
The integral of sin(x)-12cos(x) is -cos(x)-12sin(x)+C