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)

Add a constant to the solution

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

\int \frac{1}{2 + x - 1} d x

\int x (x + 3) d x

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

\int (4 x^{5} + 5 x^{3} + 11) d x

\int cos^{3} (\frac{1}{2} 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