What is the integral of 24x^2-2sin(x) ?

The integral of 24x^2-2sin(x) is 8x^3+2cos(x)+C

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integral of 24x^2-2sin(x)

\int 24 x^{2} - 2 sin (x) d x

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

Solution steps

\int 24 x^{2} - 2 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 24 x^{2} d x - \int 2 sin (x) d x

\int 24 x^{2} d x = 8 x^{3}

\int 2 sin (x) d x = - 2 cos (x)

= 8 x^{3} - (- 2 cos (x))

Simplify

= 8 x^{3} + 2 cos (x)

Add a constant to the solution

= 8 x^{3} + 2 cos (x) + C

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What is the integral of 24x^2-2sin(x) ?
The integral of 24x^2-2sin(x) is 8x^3+2cos(x)+C