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

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\int \frac{x + 1}{x ^{2} - 2 x + 5} d x

\int \frac{x ^{2} + 1}{( x + 1 ) ^{2} ( x - 1 ) ^{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