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

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

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

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

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

Solution steps

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

Expand

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

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

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

\int 3 d x = 3 x

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

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

Add a constant to the solution

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

\frac{d}{d t} (cos^{2} (t))

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

\frac{d}{d t} (9 cos (t) - cos (9 t))

\int e^{\frac{4 x}{3}} (\frac{4}{3}) d x

- \frac{3 y}{3 x + 2 y}

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