What is the integral of (cos(x)+1/4 x) ?

The integral of (cos(x)+1/4 x) is sin(x)+(x^2)/8+C

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integral of (cos(x)+1/4 x)

\int (cos (x) + \frac{1}{4} x) d x

sin (x) + \frac{x ^{2}}{8} + C

Solution steps

\int cos (x) + \frac{1}{4} 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}{4} x d x

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

\int \frac{1}{4} x d x = \frac{x ^{2}}{8}

= sin (x) + \frac{x ^{2}}{8}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{8} + C

\int sin^{23} (x) d x

x \to - 4 + lim (5 x + 20 - 8)

n = 0 \sum \infty - 1^{n}

\int \frac{2 x + 1}{x ^{2} + 2 x + 122} d x

\frac{\partial}{\partial y} (x^{2} y + y)

What is the integral of (cos(x)+1/4 x) ?
The integral of (cos(x)+1/4 x) is sin(x)+(x^2)/8+C