What is the integral of 6x^2-5x+3 ?

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

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integral of 6x^2-5x+3

\int 6 x^{2} - 5 x + 3 d x

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

Solution steps

\int 6 x^{2} - 5 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 6 x^{2} d x - \int 5 x d x + \int 3 d x

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\int (6 sin (2 x) - 4 cos (4 x)) d x

y^{2} = 4 x, 4 x - 3 y = 4

(arctan (9 x))^{2}

\frac{1}{x ^{5}}

9 e^{- x} - 3 e^{- 4 x}

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