What is the integral of 10x^9-12x^3-5 ?

The integral of 10x^9-12x^3-5 is x^{10}-3x^4-5x+C

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integral of 10x^9-12x^3-5

\int 10 x^{9} - 12 x^{3} - 5 d x

x^{10} - 3 x^{4} - 5 x + C

Solution steps

\int 10 x^{9} - 12 x^{3} - 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 10 x^{9} d x - \int 12 x^{3} d x - \int 5 d x

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

\int 12 x^{3} d x = 3 x^{4}

\int 5 d x = 5 x

= x^{10} - 3 x^{4} - 5 x

Add a constant to the solution

= x^{10} - 3 x^{4} - 5 x + C

What is the integral of 10x^9-12x^3-5 ?
The integral of 10x^9-12x^3-5 is x^{10}-3x^4-5x+C