What is the integral of-cos(x)+sin(x)+7 ?

The integral of-cos(x)+sin(x)+7 is -sin(x)-cos(x)+7x+C

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integral of-cos(x)+sin(x)+7

\int - cos (x) + sin (x) + 7 d x

- sin (x) - cos (x) + 7 x + C

Solution steps

\int - cos (x) + sin (x) + 7 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 7 d x

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

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

\int 7 d x = 7 x

= - sin (x) - cos (x) + 7 x

Add a constant to the solution

= - sin (x) - cos (x) + 7 x + C

\int (\frac{x ^{2} - 3 x - 5}{x + 2}) d x

\int 6 8 x + 4 d x

\int (2 x - 1) (x^{2} - x + 3)^{3} d x

\int x - a d x

\int (12 x + 5) 6 x^{2} + 5 x d x

What is the integral of-cos(x)+sin(x)+7 ?
The integral of-cos(x)+sin(x)+7 is -sin(x)-cos(x)+7x+C