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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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