What is the integral of (sqrt(x^2-1))/(x^3) ?

The integral of (sqrt(x^2-1))/(x^3) is -(sqrt(x^2-1))/(2x^2)+1/2 arctan(sqrt(x^2-1))+C

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integral of (sqrt(x^2-1))/(x^3)

\int \frac{x ^{2} - 1}{x ^{3}} d x

- \frac{x ^{2} - 1}{2 x ^{2}} + \frac{1}{2} arctan (x^{2} - 1) + C

Solution steps

\int \frac{x ^{2} - 1}{x ^{3}} d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d y}{d t} = 6 e^{2 t - y}

\frac{d}{d x} (m x e^{n x^{2}})

\frac{d}{d x} (5 \cdot T g (T, x) (2 x^{3}) + \frac{2}{x ^{2}})

y = \frac{5}{x}, (1, 5)

\int_{\frac{6}{5}}^{4} \frac{1}{1 - x ^{2}} d x

What is the integral of (sqrt(x^2-1))/(x^3) ?
The integral of (sqrt(x^2-1))/(x^3) is -(sqrt(x^2-1))/(2x^2)+1/2 arctan(sqrt(x^2-1))+C