What is the integral of 6+3cos(x) ?

The integral of 6+3cos(x) is 6x+3sin(x)+C

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integral of 6+3cos(x)

\int 6 + 3 cos (x) d x

6 x + 3 sin (x) + C

Solution steps

\int 6 + 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 6 d x + \int 3 cos (x) d x

\int 6 d x = 6 x

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

= 6 x + 3 sin (x)

Add a constant to the solution

= 6 x + 3 sin (x) + C

\int \frac{5}{x ( x ^{4} + 7 )} d x

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

\int \frac{x - 2}{x + 1} d x

h \to 0 lim (\frac{f ( h ) ( 8 + h ) - f ( 8 )}{h})

(- 5, - 10), (- 1, 5)