What is the integral of (4x^7+5x^5-9x^2+3) ?

The integral of (4x^7+5x^5-9x^2+3) is (x^8)/2+(5x^6)/6-3x^3+3x+C

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integral of (4x^7+5x^5-9x^2+3)

\int (4 x^{7} + 5 x^{5} - 9 x^{2} + 3) d x

\frac{x ^{8}}{2} + \frac{5 x ^{6}}{6} - 3 x^{3} + 3 x + C

Solution steps

\int 4 x^{7} + 5 x^{5} - 9 x^{2} + 3 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 4 x^{7} d x + \int 5 x^{5} d x - \int 9 x^{2} d x + \int 3 d x

\int 4 x^{7} d x = \frac{x ^{8}}{2}

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

\int 9 x^{2} d x = 3 x^{3}

\int 3 d x = 3 x

= \frac{x ^{8}}{2} + \frac{5 x ^{6}}{6} - 3 x^{3} + 3 x

Add a constant to the solution

= \frac{x ^{8}}{2} + \frac{5 x ^{6}}{6} - 3 x^{3} + 3 x + C

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What is the integral of (4x^7+5x^5-9x^2+3) ?
The integral of (4x^7+5x^5-9x^2+3) is (x^8)/2+(5x^6)/6-3x^3+3x+C