What is the integral of 9x^5-3x^2+7 ?

The integral of 9x^5-3x^2+7 is (3x^6)/2-x^3+7x+C

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integral of 9x^5-3x^2+7

\int 9 x^{5} - 3 x^{2} + 7 d x

\frac{3 x ^{6}}{2} - x^{3} + 7 x + C

Solution steps

\int 9 x^{5} - 3 x^{2} + 7 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 9 x^{5} d x - \int 3 x^{2} d x + \int 7 d x

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

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

\int 7 d x = 7 x

= \frac{3 x ^{6}}{2} - x^{3} + 7 x

Add a constant to the solution

= \frac{3 x ^{6}}{2} - x^{3} + 7 x + C

What is the integral of 9x^5-3x^2+7 ?
The integral of 9x^5-3x^2+7 is (3x^6)/2-x^3+7x+C