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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Simplify

= \frac{7}{x} - \frac{2}{x ^{2}}

Add a constant to the solution

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

2 x^{3} + 6 x^{2} - 90 x - 6

\int 4 sin (x) d x

x \cdot 1 - x^{2}

h \to 0 lim \frac{( 2 ( 3 + h ) ^{4} - 162 )}{h}

\frac{d}{d x} (3 ln (7 x))

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