What is the integral of (3x+2)/(sqrt(x^2-11)) ?

The integral of (3x+2)/(sqrt(x^2-11)) is 3sqrt(x^2-11)+2ln|sqrt(1/11 (x^2-11))+1/(sqrt(11))x|+C

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integral of (3x+2)/(sqrt(x^2-11))

\int \frac{3 x + 2}{x ^{2} - 11} d x

3 x^{2} - 11 + 2 ln \frac{1}{11} (x^{2} - 11) + \frac{1}{11} x + C

Solution steps

\int \frac{3 x + 2}{x ^{2} - 11} d x

Expand

\frac{3 x + 2}{x ^{2} - 11} : \frac{3 x}{x ^{2} - 11} + \frac{2}{x ^{2} - 11}

= \int \frac{3 x}{x ^{2} - 11} + \frac{2}{x ^{2} - 11} 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} - 11} d x + \int \frac{2}{x ^{2} - 11} d x

\int \frac{3 x}{x ^{2} - 11} d x = 3 x^{2} - 11

\int \frac{2}{x ^{2} - 11} d x = 2 ln \frac{1}{11} (x^{2} - 11) + \frac{1}{11} x

= 3 x^{2} - 11 + 2 ln \frac{1}{11} (x^{2} - 11) + \frac{1}{11} x

Add a constant to the solution

= 3 x^{2} - 11 + 2 ln \frac{1}{11} (x^{2} - 11) + \frac{1}{11} x + C

x \to 0 lim (\frac{sin ( 3 x )}{x})

\int x^{2} + 14 x d x

y = 2 x^{3} - 3 x^{2}

y^{^{''}} + 2 y = 0, y (0) = 1, y (1) = 0

y = arccot (t)

What is the integral of (3x+2)/(sqrt(x^2-11)) ?
The integral of (3x+2)/(sqrt(x^2-11)) is 3sqrt(x^2-11)+2ln|sqrt(1/11 (x^2-11))+1/(sqrt(11))x|+C