What is the integral of (9x^8+10x^5-5x^2-5) ?

The integral of (9x^8+10x^5-5x^2-5) is x^9+(5x^6)/3-(5x^3)/3-5x+C

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integral of (9x^8+10x^5-5x^2-5)

\int (9 x^{8} + 10 x^{5} - 5 x^{2} - 5) d x

x^{9} + \frac{5 x ^{6}}{3} - \frac{5 x ^{3}}{3} - 5 x + C

Solution steps

\int 9 x^{8} + 10 x^{5} - 5 x^{2} - 5 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^{8} d x + \int 10 x^{5} d x - \int 5 x^{2} d x - \int 5 d x

\int 9 x^{8} d x = x^{9}

\int 10 x^{5} d x = \frac{5 x ^{6}}{3}

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

\int 5 d x = 5 x

= x^{9} + \frac{5 x ^{6}}{3} - \frac{5 x ^{3}}{3} - 5 x

Add a constant to the solution

= x^{9} + \frac{5 x ^{6}}{3} - \frac{5 x ^{3}}{3} - 5 x + C

\int e^{- 3 x} + ln (3) - \frac{1}{x} d x

\frac{d y}{d x} = - \frac{( 2 x ^{2} + y )}{( x ^{2} y - x )}

\frac{\partial}{\partial x} (e^{t} cos (x))

7 x^{3} + 5 x^{2} + 4 x

x \to \frac{2}{π} lim (cos (x))

What is the integral of (9x^8+10x^5-5x^2-5) ?
The integral of (9x^8+10x^5-5x^2-5) is x^9+(5x^6)/3-(5x^3)/3-5x+C