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

e^{3 x}, 9

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\frac{d}{d x} (x arccos (\frac{1}{x}))