What is the integral of 2x^2-8cos(x) ?

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

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integral of 2x^2-8cos(x)

\int 2 x^{2} - 8 cos (x) d x

\frac{2 x ^{3}}{3} - 8 sin (x) + C

Solution steps

\int 2 x^{2} - 8 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 2 x^{2} d x - \int 8 cos (x) d x

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

\int 8 cos (x) d x = 8 sin (x)

= \frac{2 x ^{3}}{3} - 8 sin (x)

Add a constant to the solution

= \frac{2 x ^{3}}{3} - 8 sin (x) + C

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