What is the integral of (2+5/7 x-6x^2) ?

The integral of (2+5/7 x-6x^2) is 2x+(5x^2)/(14)-2x^3+C

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integral of (2+5/7 x-6x^2)

\int (2 + \frac{5}{7} x - 6 x^{2}) d x

2 x + \frac{5 x ^{2}}{14} - 2 x^{3} + C

Solution steps

\int 2 + \frac{5}{7} x - 6 x^{2} 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 2 d x + \int \frac{5}{7} x d x - \int 6 x^{2} d x

\int 2 d x = 2 x

\int \frac{5}{7} x d x = \frac{5 x ^{2}}{14}

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

= 2 x + \frac{5 x ^{2}}{14} - 2 x^{3}

Add a constant to the solution

= 2 x + \frac{5 x ^{2}}{14} - 2 x^{3} + C

What is the integral of (2+5/7 x-6x^2) ?
The integral of (2+5/7 x-6x^2) is 2x+(5x^2)/(14)-2x^3+C