What is the integral of ((3x^2-5x+7))/(x^4) ?

The integral of ((3x^2-5x+7))/(x^4) is -3/x+5/(2x^2)-7/(3x^3)+C

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integral of ((3x^2-5x+7))/(x^4)

\int \frac{( 3 x ^{2} - 5 x + 7 )}{x ^{4}} d x

- \frac{3}{x} + \frac{5}{2 x ^{2}} - \frac{7}{3 x ^{3}} + C

Solution steps

\int \frac{3 x ^{2} - 5 x + 7}{x ^{4}} d x

Expand

\frac{3 x ^{2} - 5 x + 7}{x ^{4}} : \frac{3}{x ^{2}} - \frac{5}{x ^{3}} + \frac{7}{x ^{4}}

= \int \frac{3}{x ^{2}} - \frac{5}{x ^{3}} + \frac{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 \frac{3}{x ^{2}} d x - \int \frac{5}{x ^{3}} d x + \int \frac{7}{x ^{4}} d x

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

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

\int \frac{7}{x ^{4}} d x = - \frac{7}{3 x ^{3}}

= - \frac{3}{x} - (- \frac{5}{2 x ^{2}}) - \frac{7}{3 x ^{3}}

Simplify

= - \frac{3}{x} + \frac{5}{2 x ^{2}} - \frac{7}{3 x ^{3}}

Add a constant to the solution

= - \frac{3}{x} + \frac{5}{2 x ^{2}} - \frac{7}{3 x ^{3}} + C

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What is the integral of ((3x^2-5x+7))/(x^4) ?
The integral of ((3x^2-5x+7))/(x^4) is -3/x+5/(2x^2)-7/(3x^3)+C