What is the integral of sin(x)+7cos(x)-1 ?

The integral of sin(x)+7cos(x)-1 is -cos(x)+7sin(x)-x+C

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integral of sin(x)+7cos(x)-1

\int sin (x) + 7 cos (x) - 1 d x

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

Solution steps

\int sin (x) + 7 cos (x) - 1 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 sin (x) d x + \int 7 cos (x) d x - \int 1 d x

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

\int 7 cos (x) d x = 7 sin (x)

\int 1 d x = x

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

Add a constant to the solution

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

What is the integral of sin(x)+7cos(x)-1 ?
The integral of sin(x)+7cos(x)-1 is -cos(x)+7sin(x)-x+C