What is the integral of (x^2-7x+4) ?

The integral of (x^2-7x+4) is (x^3)/3-(7x^2)/2+4x+C

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integral of (x^2-7x+4)

\int (x^{2} - 7 x + 4) d x

\frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 4 x + C

Solution steps

\int x^{2} - 7 x + 4 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 7 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{7 x ^{2}}{2} + 4 x + C

y^{^{''}} + 4 y^{^{'}} + 4 y = (5 + x) e^{- 2 x}

\frac{d y}{d x} + \frac{y}{x} = e^{x}

\frac{d}{d x} (d - b + \frac{- a x ^{3} - d}{x ^{2}})

\frac{d}{d x} (e^{2 x} + e^{- 3 x})

\frac{d x}{d y} = x (1 - x)

What is the integral of (x^2-7x+4) ?
The integral of (x^2-7x+4) is (x^3)/3-(7x^2)/2+4x+C