What is the integral of (2+3x^3-8x^3) ?

The integral of (2+3x^3-8x^3) is 2x-(5x^4)/4+C

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integral of (2+3x^3-8x^3)

\int (2 + 3 x^{3} - 8 x^{3}) d x

2 x - \frac{5 x ^{4}}{4} + C

Solution steps

\int 2 + 3 x^{3} - 8 x^{3} d x

Simplify

= \int 2 - 5 x^{3} 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 d x - \int 5 x^{3} d x

\int 2 d x = 2 x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

= 2 x - \frac{5 x ^{4}}{4}

Add a constant to the solution

= 2 x - \frac{5 x ^{4}}{4} + C

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What is the integral of (2+3x^3-8x^3) ?
The integral of (2+3x^3-8x^3) is 2x-(5x^4)/4+C