What is the integral of (x^4-2x^3+1)/(x^2) ?

The integral of (x^4-2x^3+1)/(x^2) is (x^3)/3-x^2-1/x+C

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integral of (x^4-2x^3+1)/(x^2)

\int \frac{x ^{4} - 2 x ^{3} + 1}{x ^{2}} d x

\frac{x ^{3}}{3} - x^{2} - \frac{1}{x} + C

Solution steps

\int \frac{x ^{4} - 2 x ^{3} + 1}{x ^{2}} d x

Expand

\frac{x ^{4} - 2 x ^{3} + 1}{x ^{2}} : x^{2} - 2 x + \frac{1}{x ^{2}}

= \int x^{2} - 2 x + \frac{1}{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 x^{2} d x - \int 2 x d x + \int \frac{1}{x ^{2}} d x

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

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

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= \frac{x ^{3}}{3} - x^{2} - \frac{1}{x}

Add a constant to the solution

= \frac{x ^{3}}{3} - x^{2} - \frac{1}{x} + C

f (x) = (3 x)^{2 x}

\frac{( 3 x ^{2} + 2 x + 7 )}{( x + 1 )}

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

f (x) = sin (x), 0, π

\frac{1}{8 x ^{2}}, x, \frac{x}{20}

What is the integral of (x^4-2x^3+1)/(x^2) ?
The integral of (x^4-2x^3+1)/(x^2) is (x^3)/3-x^2-1/x+C