What is the integral of 1/(x^2sqrt(x^2-144)) ?

The integral of 1/(x^2sqrt(x^2-144)) is (sqrt(x^2-144))/(144x)+C

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integral of 1/(x^2sqrt(x^2-144))

\int \frac{1}{x ^{2} x ^{2} - 144} d x

\frac{x ^{2} - 144}{144 x} + C

Solution steps

\int \frac{1}{x ^{2} x ^{2} - 144} d x

Apply Trigonometric Substitution

: \int \frac{1}{144 sec ( u )} d u

= \int \frac{1}{144 sec ( u )} d u

Take the constant out:

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

= \frac{1}{144} \cdot \int \frac{1}{sec ( u )} d u

Rewrite using trig identities

= \frac{1}{144} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{144} sin (u)

Substitute back

u = arcsec (\frac{1}{12} x)

= \frac{1}{144} sin (arcsec (\frac{1}{12} x))

Simplify

\frac{1}{144} sin (arcsec (\frac{1}{12} x)) : \frac{x ^{2} - 144}{144 x}

= \frac{x ^{2} - 144}{144 x}

Add a constant to the solution

= \frac{x ^{2} - 144}{144 x} + C

\int_{- π}^{0} 1 d x

x \to 0 lim (\frac{sin ( 3 x )}{x + 4 - 2})

\frac{d}{d x} (x^{4} - 5 x + 1)

\int_{0}^{3} 2 π (5 - x) (9 - x^{2}) d x

arcsin (x)

What is the integral of 1/(x^2sqrt(x^2-144)) ?
The integral of 1/(x^2sqrt(x^2-144)) is (sqrt(x^2-144))/(144x)+C