What is the integral of 3x^5-x^2+4x-1 ?

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

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integral of 3x^5-x^2+4x-1

\int 3 x^{5} - x^{2} + 4 x - 1 d x

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

Solution steps

\int 3 x^{5} - x^{2} + 4 x - 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 3 x^{5} d x - \int x^{2} d x + \int 4 x d x - \int 1 d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

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

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

\int 1 d x = x

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

Add a constant to the solution

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

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