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

The integral of (2x^2+7x-8)/(x-7) is x^2+21x+139ln|x-7|-196+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x^{2} + 21 x + 139 ln ∣ x - 7 ∣ - 196 + C

Solution steps

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

Apply u-substitution

: \int \frac{2 u ^{2} + 35 u + 139}{u} d u

= \int \frac{2 u ^{2} + 35 u + 139}{u} d u

Expand

\frac{2 u ^{2} + 35 u + 139}{u} : 2 u + 35 + \frac{139}{u}

= \int 2 u + 35 + \frac{139}{u} d u

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 u d u + \int 35 d u + \int \frac{139}{u} d u

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

\int 35 d u = 35 u

\int \frac{139}{u} d u = 139 ln ∣ u ∣

= u^{2} + 35 u + 139 ln ∣ u ∣

Substitute back

u = x - 7

= (x - 7)^{2} + 35 (x - 7) + 139 ln ∣ x - 7 ∣

Simplify

(x - 7)^{2} + 35 (x - 7) + 139 ln ∣ x - 7 ∣ : x^{2} + 21 x + 139 ln ∣ x - 7 ∣ - 196

= x^{2} + 21 x + 139 ln ∣ x - 7 ∣ - 196

Add a constant to the solution

= x^{2} + 21 x + 139 ln ∣ x - 7 ∣ - 196 + C

\frac{\partial}{\partial y} (e^{2 x + 3 y})

x \to 1 + lim (x + 2)

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

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

n = 1 \sum \infty - 30 n

What is the integral of (2x^2+7x-8)/(x-7) ?
The integral of (2x^2+7x-8)/(x-7) is x^2+21x+139ln|x-7|-196+C