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

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

\frac{\partial}{\partial y} (x^{y} + y^{x})

\frac{\partial}{\partial x} (1 + cos (y))

x \to 0 lim (1 - cos^{3} (x))

(2 y - x^{3}) d x = x d y

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