What is the integral of ((3x-1))/(sqrt(x^2-9)) ?

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

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integral of ((3x-1))/(sqrt(x^2-9))

\int \frac{( 3 x - 1 )}{x ^{2} - 9} d x

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

Solution steps

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

Expand

\frac{3 x - 1}{x ^{2} - 9} : \frac{3 x}{x ^{2} - 9} - \frac{1}{x ^{2} - 9}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{1}{2 ^{n} + 2 n}

\int \frac{x ^{3} - 27}{x - 3} d x

\int_{2}^{5} 6 x d x

y^{^{'}} + 2 y = e^{- 2 t}

x \to 0 lim ((e^{x} + x)^{\frac{2}{x}})

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