What is the integral of (7x^3-5x^2+7x-8)/(x^2) ?

The integral of (7x^3-5x^2+7x-8)/(x^2) is (7x^2)/2-5x+7ln|x|+8/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (7x^3-5x^2+7x-8)/(x^2)

\int \frac{7 x ^{3} - 5 x ^{2} + 7 x - 8}{x ^{2}} d x

\frac{7 x ^{2}}{2} - 5 x + 7 ln ∣ x ∣ + \frac{8}{x} + C

Solution steps

\int \frac{7 x ^{3} - 5 x ^{2} + 7 x - 8}{x ^{2}} d x

Expand

\frac{7 x ^{3} - 5 x ^{2} + 7 x - 8}{x ^{2}} : 7 x - 5 + \frac{7}{x} - \frac{8}{x ^{2}}

= \int 7 x - 5 + \frac{7}{x} - \frac{8}{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 7 x d x - \int 5 d x + \int \frac{7}{x} d x - \int \frac{8}{x ^{2}} d x

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

\int 5 d x = 5 x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{8}{x ^{2}} d x = - \frac{8}{x}

= \frac{7 x ^{2}}{2} - 5 x + 7 ln ∣ x ∣ - (- \frac{8}{x})

Simplify

= \frac{7 x ^{2}}{2} - 5 x + 7 ln ∣ x ∣ + \frac{8}{x}

Add a constant to the solution

= \frac{7 x ^{2}}{2} - 5 x + 7 ln ∣ x ∣ + \frac{8}{x} + C

\int \frac{x ^{3}}{x ^{2} - x - 6} d x

\int \frac{7 x ^{2} - x - 5}{x ^{2} - 1} d x

\int 5 cos (9 t) d t

\int \frac{1}{x 4 x + 81} d x

What is the integral of (7x^3-5x^2+7x-8)/(x^2) ?
The integral of (7x^3-5x^2+7x-8)/(x^2) is (7x^2)/2-5x+7ln|x|+8/x+C