What is the integral of cos(x)+18x ?

The integral of cos(x)+18x is sin(x)+9x^2+C

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integral of cos(x)+18x

\int cos (x) + 18 x d x

sin (x) + 9 x^{2} + C

Solution steps

\int cos (x) + 18 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 cos (x) d x + \int 18 x d x

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

\int 18 x d x = 9 x^{2}

= sin (x) + 9 x^{2}

Add a constant to the solution

= sin (x) + 9 x^{2} + C

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What is the integral of cos(x)+18x ?
The integral of cos(x)+18x is sin(x)+9x^2+C