What is the integral of 8x-cos(x) ?

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

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integral of 8x-cos(x)

\int 8 x - cos (x) d x

4 x^{2} - sin (x) + C

Solution steps

\int 8 x - cos (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 8 x d x - \int cos (x) d x

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

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

= 4 x^{2} - sin (x)

Add a constant to the solution

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

\frac{d}{d x} (2 cos (x))

\frac{d}{d x} ((sin (x^{2}) + x^{2}) (cos (x) - 3 x))

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

\int 4 x^{3} e^{- 5 x} d x