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

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

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

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

sin (x) - cos (x) + C

Solution steps

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

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

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

= sin (x) - cos (x)

Add a constant to the solution

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

\frac{d}{d x} (a sin (5 x))

x \to - 3 lim (\frac{x ^{2}}{x ^{2} - 9})

\frac{\partial}{\partial x} (x sin (x^{2} - y^{2}))

(x + y e^{\frac{y}{x}}) d x - (x e^{\frac{y}{x}}) d y = 0

\frac{d}{d x} (\frac{- x ^{2} - 5}{( x ^{2} - 5 ) ^{2}})

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