What is the integral of 1/((11-10x-x^2)^2) ?

The integral of 1/((11-10x-x^2)^2) is -1/864 ln|x-1|-1/(144(x-1))+1/864 ln|x+11|-1/(144(x+11))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((11-10x-x^2)^2)

\int \frac{1}{( 11 - 10 x - x ^{2} ) ^{2}} d x

- \frac{1}{864} ln ∣ x - 1 ∣ - \frac{1}{144 ( x - 1 )} + \frac{1}{864} ln ∣ x + 11 ∣ - \frac{1}{144 ( x + 11 )} + C

Solution steps

\int \frac{1}{( 11 - 10 x - x ^{2} ) ^{2}} d x

Take the partial fraction of

\frac{1}{( 11 - 10 x - x ^{2} ) ^{2}} : - \frac{1}{864 ( x - 1 )} + \frac{1}{144 ( x - 1 ) ^{2}} + \frac{1}{864 ( x + 11 )} + \frac{1}{144 ( x + 11 ) ^{2}}

= \int - \frac{1}{864 ( x - 1 )} + \frac{1}{144 ( x - 1 ) ^{2}} + \frac{1}{864 ( x + 11 )} + \frac{1}{144 ( x + 11 ) ^{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 \frac{1}{864 ( x - 1 )} d x + \int \frac{1}{144 ( x - 1 ) ^{2}} d x + \int \frac{1}{864 ( x + 11 )} d x + \int \frac{1}{144 ( x + 11 ) ^{2}} d x

\int \frac{1}{864 ( x - 1 )} d x = \frac{1}{864} ln ∣ x - 1 ∣

\int \frac{1}{144 ( x - 1 ) ^{2}} d x = - \frac{1}{144 ( x - 1 )}

\int \frac{1}{864 ( x + 11 )} d x = \frac{1}{864} ln ∣ x + 11 ∣

\int \frac{1}{144 ( x + 11 ) ^{2}} d x = - \frac{1}{144 ( x + 11 )}

= - \frac{1}{864} ln ∣ x - 1 ∣ - \frac{1}{144 ( x - 1 )} + \frac{1}{864} ln ∣ x + 11 ∣ - \frac{1}{144 ( x + 11 )}

Add a constant to the solution

= - \frac{1}{864} ln ∣ x - 1 ∣ - \frac{1}{144 ( x - 1 )} + \frac{1}{864} ln ∣ x + 11 ∣ - \frac{1}{144 ( x + 11 )} + C

\frac{d}{d x} (\frac{5}{x + 3})

x \to + 0 lim ((1 - 2 x)^{\frac{1}{2}})

(sin (x))^{2 x}

\int \frac{3 x + 1}{x ^{2} + 4 x + 3} d x

\int tan (x) sec^{4} (x) d x

What is the integral of 1/((11-10x-x^2)^2) ?
The integral of 1/((11-10x-x^2)^2) is -1/864 ln|x-1|-1/(144(x-1))+1/864 ln|x+11|-1/(144(x+11))+C