What is the integral of 1/(x^2sqrt(x^2-121)) ?

The integral of 1/(x^2sqrt(x^2-121)) is (sqrt(x^2-121))/(121x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x^2sqrt(x^2-121))

\int \frac{1}{x ^{2} x ^{2} - 121} d x

\frac{x ^{2} - 121}{121 x} + C

Solution steps

\int \frac{1}{x ^{2} x ^{2} - 121} d x

Apply Trigonometric Substitution

: \int \frac{1}{121 sec ( u )} d u

= \int \frac{1}{121 sec ( u )} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{121} \cdot \int \frac{1}{sec ( u )} d u

Rewrite using trig identities

= \frac{1}{121} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{121} sin (u)

Substitute back

u = arcsec (\frac{1}{11} x)

= \frac{1}{121} sin (arcsec (\frac{1}{11} x))

Simplify

\frac{1}{121} sin (arcsec (\frac{1}{11} x)) : \frac{x ^{2} - 121}{121 x}

= \frac{x ^{2} - 121}{121 x}

Add a constant to the solution

= \frac{x ^{2} - 121}{121 x} + C

\frac{d}{d x} (\frac{1 - c x}{1 + c x})

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

\frac{d y}{d x} = \frac{1}{3} x^{3}

13

\int sec^{2} (x) ln (tan (x)) d x

What is the integral of 1/(x^2sqrt(x^2-121)) ?
The integral of 1/(x^2sqrt(x^2-121)) is (sqrt(x^2-121))/(121x)+C