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

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

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integral of (cos(θ)+sin(θ))

\int (cos (θ) + sin (θ)) d θ

sin (θ) - cos (θ) + C

Solution steps

\int cos (θ) + sin (θ) d θ

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 (θ) d θ + \int sin (θ) d θ

\int cos (θ) d θ = sin (θ)

\int sin (θ) d θ = - cos (θ)

= sin (θ) - cos (θ)

Add a constant to the solution

= sin (θ) - cos (θ) + C

\int (\frac{2 x ^{2} + 7 x - 3}{x - 2}) d x

\int \frac{2 x}{2 + x} d x

\int - cos (π + y) + cos (y) d y

\int (x + 2) 3 x^{2} + 4 x d x

\int \frac{1}{( arctan ( \frac{y}{7} ) ) ( 49 + y ^{2} )} d y

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