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

\int_{4}^{7} x^{4} ln (2 x) d x

x \to 8 lim (\frac{x ^{8}}{x - 8})

\int - \frac{10}{t + 7} d t

\frac{d}{d x} (3 x^{2} + 8 x)

\frac{d y}{d x} = 6 x^{2} - x^{2} y

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