What is the integral of (cos(x)+1/2 x) ?

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

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integral of (cos(x)+1/2 x)

\int (cos (x) + \frac{1}{2} x) d x

sin (x) + \frac{x ^{2}}{4} + C

Solution steps

\int cos (x) + \frac{1}{2} 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}{2} x d x

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

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

= sin (x) + \frac{x ^{2}}{4}

Add a constant to the solution

= sin (x) + \frac{x ^{2}}{4} + C

tan (2 x)

g (t) = \frac{t - t}{t ^{\frac{1}{6}}}

\frac{d y}{d x} - y = \frac{e ^{x}}{y}

\frac{\partial}{\partial x} ((x^{2})^{- \frac{1}{2}})

u (x) = 3 x^{2} - x + 6

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