What is the integral of sin(x)+12x ?

The integral of sin(x)+12x is -cos(x)+6x^2+C

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integral of sin(x)+12x

\int sin (x) + 12 x d x

- cos (x) + 6 x^{2} + C

Solution steps

\int sin (x) + 12 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 sin (x) d x + \int 12 x d x

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

\int 12 x d x = 6 x^{2}

= - cos (x) + 6 x^{2}

Add a constant to the solution

= - cos (x) + 6 x^{2} + C

\frac{d}{d x} (16 x^{3})

f (x) = \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

\frac{d y}{d x} = y - 5

\frac{d}{d x} (\frac{lo g _{2} ( x )}{x})

\frac{x ^{2}}{x - 4}

What is the integral of sin(x)+12x ?
The integral of sin(x)+12x is -cos(x)+6x^2+C