What is the integral of (4cos(x)+5sin(x)) ?

The integral of (4cos(x)+5sin(x)) is 4sin(x)-5cos(x)+C

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integral of (4cos(x)+5sin(x))

\int (4 cos (x) + 5 sin (x)) d x

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

Solution steps

\int 4 cos (x) + 5 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 4 cos (x) d x + \int 5 sin (x) d x

\int 4 cos (x) d x = 4 sin (x)

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

= 4 sin (x) - 5 cos (x)

Add a constant to the solution

= 4 sin (x) - 5 cos (x) + C

\frac{\partial}{\partial x} (x^{x^{2} - y^{2}})

\frac{d}{d x} (\frac{( - 2 x ^{2} + 2 x )}{( 3 x - 3 )})

\frac{d}{d x} (\frac{40}{3 x ^{\frac{1}{3}}})

x \to 0 lim (\frac{x + 4 - 2}{sin ( 5 x )})

\int 39 arctan (x) d x

What is the integral of (4cos(x)+5sin(x)) ?
The integral of (4cos(x)+5sin(x)) is 4sin(x)-5cos(x)+C