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

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

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integral of sin(θ)+cos(θ)

\int sin (θ) + cos (θ) d θ

- cos (θ) + sin (θ) + C

Solution steps

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

\int sin (θ) d θ = - cos (θ)

\int cos (θ) d θ = sin (θ)

= - cos (θ) + sin (θ)

Add a constant to the solution

= - cos (θ) + sin (θ) + C

x \to 5 lim (4)

x^{8 c o s (x)}

x y^{^{'}} + (1 + 6 x) y = 24 e^{- 6 x}

\int \frac{1}{4 x + 7} d x

\int \frac{8 arcsin ( x )}{x ^{2}} d x

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