What is the integral of cos(x)+1/3 x ?

The integral of cos(x)+1/3 x is sin(x)+(x^2)/6+C

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integral of cos(x)+1/3 x

\int cos (x) + \frac{1}{3} x d x

sin (x) + \frac{x ^{2}}{6} + C

Solution steps

\int cos (x) + \frac{1}{3} 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 \frac{1}{3} x d x

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

\int \frac{1}{3} x d x = \frac{x ^{2}}{6}

= sin (x) + \frac{x ^{2}}{6}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{6} + C

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What is the integral of cos(x)+1/3 x ?
The integral of cos(x)+1/3 x is sin(x)+(x^2)/6+C