What is the integral of 5x^4-2x^2+10x-3 ?

The integral of 5x^4-2x^2+10x-3 is x^5-(2x^3)/3+5x^2-3x+C

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integral of 5x^4-2x^2+10x-3

\int 5 x^{4} - 2 x^{2} + 10 x - 3 d x

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

Solution steps

\int 5 x^{4} - 2 x^{2} + 10 x - 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 5 x^{4} d x - \int 2 x^{2} d x + \int 10 x d x - \int 3 d x

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

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

\int 10 x d x = 5 x^{2}

\int 3 d x = 3 x

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

Add a constant to the solution

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

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