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

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

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integral of 2cos(x)-sin(x)

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

2 sin (x) + cos (x) + C

Solution steps

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

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

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

= 2 sin (x) - (- cos (x))

Simplify

= 2 sin (x) + cos (x)

Add a constant to the solution

= 2 sin (x) + cos (x) + C

n = 1 \sum \infty cos (\frac{1}{n ^{2}})

\frac{d}{d t} (g (t))

n = 0 \sum \infty (\frac{8}{9})^{n}

x \to 0 lim (\frac{tan ( x )}{4 x})

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

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