What is the integral of (2x^5-7x^3+6) ?

The integral of (2x^5-7x^3+6) is (x^6)/3-(7x^4)/4+6x+C

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integral of (2x^5-7x^3+6)

\int (2 x^{5} - 7 x^{3} + 6) d x

\frac{x ^{6}}{3} - \frac{7 x ^{4}}{4} + 6 x + C

Solution steps

\int 2 x^{5} - 7 x^{3} + 6 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^{5} d x - \int 7 x^{3} d x + \int 6 d x

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

\int 7 x^{3} d x = \frac{7 x ^{4}}{4}

\int 6 d x = 6 x

= \frac{x ^{6}}{3} - \frac{7 x ^{4}}{4} + 6 x

Add a constant to the solution

= \frac{x ^{6}}{3} - \frac{7 x ^{4}}{4} + 6 x + C

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What is the integral of (2x^5-7x^3+6) ?
The integral of (2x^5-7x^3+6) is (x^6)/3-(7x^4)/4+6x+C