What is the integral of (3cos(x)-7sin(x)) ?

The integral of (3cos(x)-7sin(x)) is 3sin(x)+7cos(x)+C

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integral of (3cos(x)-7sin(x))

\int (3 cos (x) - 7 sin (x)) d x

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

Solution steps

\int 3 cos (x) - 7 sin (x) 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 3 cos (x) d x - \int 7 sin (x) d x

\int 3 cos (x) d x = 3 sin (x)

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

= 3 sin (x) - (- 7 cos (x))

Simplify

= 3 sin (x) + 7 cos (x)

Add a constant to the solution

= 3 sin (x) + 7 cos (x) + C

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What is the integral of (3cos(x)-7sin(x)) ?
The integral of (3cos(x)-7sin(x)) is 3sin(x)+7cos(x)+C