What is the integral of 10x^9+10x^5-2x^4-1 ?

The integral of 10x^9+10x^5-2x^4-1 is x^{10}+(5x^6)/3-(2x^5)/5-x+C

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integral of 10x^9+10x^5-2x^4-1

\int 10 x^{9} + 10 x^{5} - 2 x^{4} - 1 d x

x^{10} + \frac{5 x ^{6}}{3} - \frac{2 x ^{5}}{5} - x + C

Solution steps

\int 10 x^{9} + 10 x^{5} - 2 x^{4} - 1 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 10 x^{9} d x + \int 10 x^{5} d x - \int 2 x^{4} d x - \int 1 d x

\int 10 x^{9} d x = x^{10}

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

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

\int 1 d x = x

= x^{10} + \frac{5 x ^{6}}{3} - \frac{2 x ^{5}}{5} - x

Add a constant to the solution

= x^{10} + \frac{5 x ^{6}}{3} - \frac{2 x ^{5}}{5} - x + C

\frac{1}{x ^{8}}

sin (x) ln (sec (x) + tan (x)) - 1

x^{- 2}, 7

\frac{d}{d x} (\frac{7}{1 + 7 x})

x \to 6 lim (\frac{x ^{2} - 5}{x - 6})

What is the integral of 10x^9+10x^5-2x^4-1 ?
The integral of 10x^9+10x^5-2x^4-1 is x^{10}+(5x^6)/3-(2x^5)/5-x+C