What is the integral of cos(x)-sin(x)+3 ?

The integral of cos(x)-sin(x)+3 is sin(x)+cos(x)+3x+C

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integral of cos(x)-sin(x)+3

\int cos (x) - sin (x) + 3 d x

sin (x) + cos (x) + 3 x + C

Solution steps

\int cos (x) - sin (x) + 3 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 cos (x) d x - \int sin (x) d x + \int 3 d x

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

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

\int 3 d x = 3 x

= sin (x) - (- cos (x)) + 3 x

Simplify

= sin (x) + cos (x) + 3 x

Add a constant to the solution

= sin (x) + cos (x) + 3 x + C

\int cos (π) x cos (4 π) x d x

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

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

\int (2 + 3 x) x d x

\int \frac{1}{I ( N - I )} d I

What is the integral of cos(x)-sin(x)+3 ?
The integral of cos(x)-sin(x)+3 is sin(x)+cos(x)+3x+C