What is the integral of ((sqrt(x^2-1))/(x^4)) ?

The integral of ((sqrt(x^2-1))/(x^4)) is -(sqrt(x^2-1))/(3x^3)+(sqrt(x^2-1))/(3x)+C

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integral of ((sqrt(x^2-1))/(x^4))

\int (\frac{x ^{2} - 1}{x ^{4}}) d x

- \frac{x ^{2} - 1}{3 x ^{3}} + \frac{x ^{2} - 1}{3 x} + C

Solution steps

\int \frac{x ^{2} - 1}{x ^{4}} d x

Apply Integration By Parts

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

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

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

= - \frac{x ^{2} - 1}{3 x ^{3}} - (- \frac{x ^{2} - 1}{3 x})

Simplify

= - \frac{x ^{2} - 1}{3 x ^{3}} + \frac{x ^{2} - 1}{3 x}

Add a constant to the solution

= - \frac{x ^{2} - 1}{3 x ^{3}} + \frac{x ^{2} - 1}{3 x} + C

(x^{2} + 5) y^{^{'}} = x y

y = 3 x^{2}, (0, 1)

\frac{d}{d x} ((x^{3} + 9) e^{x})

\int_{2}^{7} \frac{4}{8 x - 11} d x

\frac{6 x ^{2} + 2 x + 6}{x}

What is the integral of ((sqrt(x^2-1))/(x^4)) ?
The integral of ((sqrt(x^2-1))/(x^4)) is -(sqrt(x^2-1))/(3x^3)+(sqrt(x^2-1))/(3x)+C