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

The integral of (7x^3-7x+5)/(x^3-x^2) is (7x^3-7x+5}{x(x-1)}+5ln|x-1|-5/(x-1)+2ln|x|+\frac{10)/x+C

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

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

\frac{7 x ^{3} - 7 x + 5}{x ( x - 1 )} + 5 ln ∣ x - 1 ∣ - \frac{5}{x - 1} + 2 ln ∣ x ∣ + \frac{10}{x} + C

Solution steps

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

Apply Integration By Parts

: \frac{7 x ^{3} - 7 x + 5}{x ( x - 1 )} - \int - \frac{7 x ^{3} - 14 x ^{2} + 22 x - 10}{x ^{2} ( x - 1 ) ^{2}} d x

= \frac{7 x ^{3} - 7 x + 5}{x ( x - 1 )} - \int - \frac{7 x ^{3} - 14 x ^{2} + 22 x - 10}{x ^{2} ( x - 1 ) ^{2}} d x

\int - \frac{7 x ^{3} - 14 x ^{2} + 22 x - 10}{x ^{2} ( x - 1 ) ^{2}} d x = - 5 ln ∣ x - 1 ∣ + \frac{5}{x - 1} - 2 ln ∣ x ∣ - \frac{10}{x}

= \frac{7 x ^{3} - 7 x + 5}{x ( x - 1 )} - (- 5 ln ∣ x - 1 ∣ + \frac{5}{x - 1} - 2 ln ∣ x ∣ - \frac{10}{x})

Simplify

= \frac{7 x ^{3} - 7 x + 5}{x ( x - 1 )} + 5 ln ∣ x - 1 ∣ - \frac{5}{x - 1} + 2 ln ∣ x ∣ + \frac{10}{x}

Add a constant to the solution

= \frac{7 x ^{3} - 7 x + 5}{x ( x - 1 )} + 5 ln ∣ x - 1 ∣ - \frac{5}{x - 1} + 2 ln ∣ x ∣ + \frac{10}{x} + C

\frac{d}{d x} (\frac{20}{x})

x \to m + lim (x - [x])

\frac{d}{d x} (arctan (e^{2 x}))

7 t^{5}

\int sec (x) (sec (x) + tan (x)) d x

What is the integral of (7x^3-7x+5)/(x^3-x^2) ?
The integral of (7x^3-7x+5)/(x^3-x^2) is (7x^3-7x+5}{x(x-1)}+5ln|x-1|-5/(x-1)+2ln|x|+\frac{10)/x+C