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

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

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integral of sin(x)+cos(x)

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

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

Solution steps

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

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

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

= - cos (x) + sin (x)

Add a constant to the solution

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

y = 2 x - \frac{2}{x}

\int (10 x + 2) 5 x^{2} + 2 x d x

x \to 0 lim (\frac{4}{x csc ( 8 x )})

\int (4 e^{x} - \frac{5}{x}) d x

x \to - 1 lim (\frac{\frac{1}{x} + 1}{x + 1})

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