What is the integral of 3x^5-8x^3+2 ?

The integral of 3x^5-8x^3+2 is (x^6)/2-2x^4+2x+C

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integral of 3x^5-8x^3+2

\int 3 x^{5} - 8 x^{3} + 2 d x

\frac{x ^{6}}{2} - 2 x^{4} + 2 x + C

Solution steps

\int 3 x^{5} - 8 x^{3} + 2 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 3 x^{5} d x - \int 8 x^{3} d x + \int 2 d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 8 x^{3} d x = 2 x^{4}

\int 2 d x = 2 x

= \frac{x ^{6}}{2} - 2 x^{4} + 2 x

Add a constant to the solution

= \frac{x ^{6}}{2} - 2 x^{4} + 2 x + C

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What is the integral of 3x^5-8x^3+2 ?
The integral of 3x^5-8x^3+2 is (x^6)/2-2x^4+2x+C