What is the integral of 6x+sin(x) ?

The integral of 6x+sin(x) is 3x^2-cos(x)+C

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integral of 6x+sin(x)

\int 6 x + sin (x) d x

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

Solution steps

\int 6 x + sin (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 6 x d x + \int sin (x) d x

\int 6 x d x = 3 x^{2}

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

= 3 x^{2} - cos (x)

Add a constant to the solution

= 3 x^{2} - cos (x) + C

\frac{\partial}{\partial y} (2 y^{2} x - 3)

\int x (x + 1)^{3} d x

\frac{d}{d x} (0.5 e^{x - 1})

x \frac{d y}{d x} + y = x y^{2}

\frac{d}{d x} (2 x^{3} - 4)