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

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

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integral of (8x^4-5x^2+2)

\int (8 x^{4} - 5 x^{2} + 2) d x

\frac{8 x ^{5}}{5} - \frac{5 x ^{3}}{3} + 2 x + C

Solution steps

\int 8 x^{4} - 5 x^{2} + 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 8 x^{4} d x - \int 5 x^{2} d x + \int 2 d x

\int 8 x^{4} d x = \frac{8 x ^{5}}{5}

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

\int 2 d x = 2 x

= \frac{8 x ^{5}}{5} - \frac{5 x ^{3}}{3} + 2 x

Add a constant to the solution

= \frac{8 x ^{5}}{5} - \frac{5 x ^{3}}{3} + 2 x + C

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