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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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

\int x arcsin (2 x^{2}) d x

n \to \infty lim (1^{n})

\int \frac{10 x}{x ^{2} + 1} d x

\frac{d}{d x} (\frac{f ( x )}{x})

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