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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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

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

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

\int (x - 1)^{- 1} d x

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