What is the integral of (sqrt(9x^2-1))/(x^2) ?

The integral of (sqrt(9x^2-1))/(x^2) is -(sqrt(9x^2-1))/x+3ln|sqrt(9x^2-1)+3x|+C

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integral of (sqrt(9x^2-1))/(x^2)

\int \frac{9 x ^{2} - 1}{x ^{2}} d x

- \frac{9 x ^{2} - 1}{x} + 3 ln 9 x^{2} - 1 + 3 x + C

Solution steps

\int \frac{9 x ^{2} - 1}{x ^{2}} d x

Apply Integration By Parts

: - \frac{9 x ^{2} - 1}{x} - \int - \frac{9}{9 x ^{2} - 1} d x

= - \frac{9 x ^{2} - 1}{x} - \int - \frac{9}{9 x ^{2} - 1} d x

\int - \frac{9}{9 x ^{2} - 1} d x = - 3 ln 9 x^{2} - 1 + 3 x

= - \frac{9 x ^{2} - 1}{x} - (- 3 ln 9 x^{2} - 1 + 3 x)

Simplify

= - \frac{9 x ^{2} - 1}{x} + 3 ln 9 x^{2} - 1 + 3 x

Add a constant to the solution

= - \frac{9 x ^{2} - 1}{x} + 3 ln 9 x^{2} - 1 + 3 x + C

\frac{d}{d x} (\frac{100}{x ^{2}})

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) - 3} d x

\int (x^{2} e^{x^{3}}) d x

\int arccos (2 x) d x

\int cos (x) \cdot cos (x) d x

What is the integral of (sqrt(9x^2-1))/(x^2) ?
The integral of (sqrt(9x^2-1))/(x^2) is -(sqrt(9x^2-1))/x+3ln|sqrt(9x^2-1)+3x|+C