What is the integral of (2/3 x^5-5/2 x+1/2) ?

The integral of (2/3 x^5-5/2 x+1/2) is (x^6)/9-(5x^2)/4+1/2 x+C

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integral of (2/3 x^5-5/2 x+1/2)

\int (\frac{2}{3} x^{5} - \frac{5}{2} x + \frac{1}{2}) d x

\frac{x ^{6}}{9} - \frac{5 x ^{2}}{4} + \frac{1}{2} x + C

Solution steps

\int \frac{2}{3} x^{5} - \frac{5}{2} x + \frac{1}{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 \frac{2}{3} x^{5} d x - \int \frac{5}{2} x d x + \int \frac{1}{2} d x

\int \frac{2}{3} x^{5} d x = \frac{x ^{6}}{9}

\int \frac{5}{2} x d x = \frac{5 x ^{2}}{4}

\int \frac{1}{2} d x = \frac{1}{2} x

= \frac{x ^{6}}{9} - \frac{5 x ^{2}}{4} + \frac{1}{2} x

Add a constant to the solution

= \frac{x ^{6}}{9} - \frac{5 x ^{2}}{4} + \frac{1}{2} x + C

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What is the integral of (2/3 x^5-5/2 x+1/2) ?
The integral of (2/3 x^5-5/2 x+1/2) is (x^6)/9-(5x^2)/4+1/2 x+C