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

\frac{d}{d x} (x^{t})

\int_{0}^{4} (2 t + 4)^{- \frac{1}{2}} d t

y^{^{'}} + 2 y = y^{2}

\int - 2 ln (\frac{3}{2} x) - cos (3 x) d x

\int \frac{x e ^{x}}{1 + e ^{x}} d x

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