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

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

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

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

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

f (x) = x^{2} + x, at x = 1, at x = 3

\frac{d}{d o} (ln (o))

x \to - 6 lim (\frac{- 5 x}{x + 6})

\frac{d y}{d x} = \frac{18 ( y - 1 )}{( 3 x - 3 ) ^{2}}, y (3) = 3

\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}}

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