What is the integral of 8x+sin(x) ?

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

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integral of 8x+sin(x)

\int 8 x + sin (x) d x

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

Solution steps

\int 8 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 8 x d x + \int sin (x) d x

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

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

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

Add a constant to the solution

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