What is the integral of cos(x)+1/8 x ?

The integral of cos(x)+1/8 x is sin(x)+(x^2)/(16)+C

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integral of cos(x)+1/8 x

\int cos (x) + \frac{1}{8} x d x

sin (x) + \frac{x ^{2}}{16} + C

Solution steps

\int cos (x) + \frac{1}{8} 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}{8} x d x

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

\int \frac{1}{8} x d x = \frac{x ^{2}}{16}

= sin (x) + \frac{x ^{2}}{16}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{16} + C

f^{^{''}} (x) = - 2 + 36 x - 12 x^{2}

- 4 sin (2 x)

f (x) = arccos (e^{- x})

x \to \frac{1}{2} lim (8 x^{3} - 1)

x \to 2 lim (\frac{x ^{2} - 4}{x - 4})

What is the integral of cos(x)+1/8 x ?
The integral of cos(x)+1/8 x is sin(x)+(x^2)/(16)+C