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

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

Popular >

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

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

- \frac{x ^{2} - 1}{x} + ln x^{2} - 1 + x + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{1}{x ^{2} - 1} d x = - ln x^{2} - 1 + x

= - \frac{x ^{2} - 1}{x} - (- ln x^{2} - 1 + x)

Simplify

= - \frac{x ^{2} - 1}{x} + ln x^{2} - 1 + x

Add a constant to the solution

= - \frac{x ^{2} - 1}{x} + ln x^{2} - 1 + x + C

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

\int 5 - \frac{x}{10000} d x

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

\int cos (x - 1) d x

\int \frac{e ^{y}}{( e ^{y} + 1 ) ^{3}} d y

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