What is the integral of cos(x)-5sin(x)-7 ?

The integral of cos(x)-5sin(x)-7 is sin(x)+5cos(x)-7x+C

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integral of cos(x)-5sin(x)-7

\int cos (x) - 5 sin (x) - 7 d x

sin (x) + 5 cos (x) - 7 x + C

Solution steps

\int cos (x) - 5 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 5 sin (x) d x - \int 7 d x

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

\int 5 sin (x) d x = - 5 cos (x)

\int 7 d x = 7 x

= sin (x) - (- 5 cos (x)) - 7 x

Simplify

= sin (x) + 5 cos (x) - 7 x

Add a constant to the solution

= sin (x) + 5 cos (x) - 7 x + C

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What is the integral of cos(x)-5sin(x)-7 ?
The integral of cos(x)-5sin(x)-7 is sin(x)+5cos(x)-7x+C