What is the integral of (2sin(x)-3cos(x)+12) ?

The integral of (2sin(x)-3cos(x)+12) is -2cos(x)-3sin(x)+12x+C

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integral of (2sin(x)-3cos(x)+12)

\int (2 sin (x) - 3 cos (x) + 12) d x

- 2 cos (x) - 3 sin (x) + 12 x + C

Solution steps

\int 2 sin (x) - 3 cos (x) + 12 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 2 sin (x) d x - \int 3 cos (x) d x + \int 12 d x

\int 2 sin (x) d x = - 2 cos (x)

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

\int 12 d x = 12 x

= - 2 cos (x) - 3 sin (x) + 12 x

Add a constant to the solution

= - 2 cos (x) - 3 sin (x) + 12 x + C

d er i v a t i v e (1 + x^{- 1})^{2}

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

\frac{d}{d x} (sin (ln (2 x)))

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

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

What is the integral of (2sin(x)-3cos(x)+12) ?
The integral of (2sin(x)-3cos(x)+12) is -2cos(x)-3sin(x)+12x+C