What is the integral of 1/(x^2sqrt(x^2-15)) ?

The integral of 1/(x^2sqrt(x^2-15)) is (sqrt(x^2-15))/(15x)+C

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integral of 1/(x^2sqrt(x^2-15))

\int \frac{1}{x ^{2} x ^{2} - 15} d x

\frac{x ^{2} - 15}{15 x} + C

Solution steps

\int \frac{1}{x ^{2} x ^{2} - 15} d x

Apply Trigonometric Substitution

: \int \frac{1}{15 sec ( u )} d u

= \int \frac{1}{15 sec ( u )} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int \frac{1}{sec ( u )} d u

Rewrite using trig identities

= \frac{1}{15} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{15} sin (u)

Substitute back

u = arcsec (\frac{1}{15} x)

= \frac{1}{15} sin (arcsec (\frac{1}{15} x))

Simplify

\frac{1}{15} sin (arcsec (\frac{1}{15} x)) : \frac{x ^{2} - 15}{15 x}

= \frac{x ^{2} - 15}{15 x}

Add a constant to the solution

= \frac{x ^{2} - 15}{15 x} + C

y = x^{2}, y = - x + 2

\frac{1}{( s - 1 ) ^{3}}

\int (9 x e^{x^{2}} + \frac{5}{x} - 5^{x} + 3 x^{2}) d x

x \to - 2 lim (n (x))

\frac{2 x ^{3}}{5 y ^{3}}

What is the integral of 1/(x^2sqrt(x^2-15)) ?
The integral of 1/(x^2sqrt(x^2-15)) is (sqrt(x^2-15))/(15x)+C