What is the integral of 1/(x^2sqrt(x^2-11)) ?

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

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integral of 1/(x^2sqrt(x^2-11))

\int \frac{1}{x ^{2} x ^{2} - 11} d x

\frac{x ^{2} - 11}{11 x} + C

Solution steps

\int \frac{1}{x ^{2} x ^{2} - 11} d x

Apply Trigonometric Substitution

: \int \frac{1}{11 sec ( u )} d u

= \int \frac{1}{11 sec ( u )} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{11} \cdot \int \frac{1}{sec ( u )} d u

Rewrite using trig identities

= \frac{1}{11} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{11} sin (u)

Substitute back

u = arcsec (\frac{1}{11} x)

= \frac{1}{11} sin (arcsec (\frac{1}{11} x))

Simplify

\frac{1}{11} sin (arcsec (\frac{1}{11} x)) : \frac{x ^{2} - 11}{11 x}

= \frac{x ^{2} - 11}{11 x}

Add a constant to the solution

= \frac{x ^{2} - 11}{11 x} + C

\frac{d}{d x} (e^{\frac{l n ( x )}{x}})

\frac{d y}{d x} = e^{9 x - 8 y}

d y + 0.15 (y - 30) d x = 0

\frac{1}{3} x^{3} - 2 x^{2} + 3 x - 4

x \to \infty lim (1 + \frac{8}{x})

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