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

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

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integral of (3x^2-5x+3)

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

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

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

\int \frac{7}{x} + \frac{1}{3 x ^{7}} d x

\int \frac{1}{2 ( x + 1 ) ^{2}} d x

\int \frac{1}{x ^{2} - 8 x - 9} d x

\int 3 x^{\frac{1}{2}} + 3 d x

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