What is the integral of-5sin(x)+3cos(x) ?

The integral of-5sin(x)+3cos(x) is 5cos(x)+3sin(x)+C

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integral of-5sin(x)+3cos(x)

\int - 5 sin (x) + 3 cos (x) d x

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

Solution steps

\int - 5 sin (x) + 3 cos (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 5 sin (x) d x + \int 3 cos (x) d x

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

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

= - (- 5 cos (x)) + 3 sin (x)

Simplify

= 5 cos (x) + 3 sin (x)

Add a constant to the solution

= 5 cos (x) + 3 sin (x) + C

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What is the integral of-5sin(x)+3cos(x) ?
The integral of-5sin(x)+3cos(x) is 5cos(x)+3sin(x)+C