What is the integral of 1/(xsqrt(x^2-12)) ?

The integral of 1/(xsqrt(x^2-12)) is 1/(2sqrt(3))arcsec(1/(2sqrt(3))x)+C

Popular >

integral of 1/(xsqrt(x^2-12))

\int \frac{1}{x x ^{2} - 12} d x

\frac{1}{2 3} arcsec (\frac{1}{2 3} x) + C

Solution steps

\int \frac{1}{x x ^{2} - 12} d x

Apply Trigonometric Substitution

: \int \frac{1}{2 3} d u

= \int \frac{1}{2 3} d u

Take the constant out:

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

= \frac{1}{2 3} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{2 3} \cdot 1 \cdot u

Substitute back

u = arcsec (\frac{1}{2 3} x)

= \frac{1}{2 3} \cdot 1 \cdot arcsec (\frac{1}{2 3} x)

Simplify

= \frac{1}{2 3} arcsec (\frac{1}{2 3} x)

Add a constant to the solution

= \frac{1}{2 3} arcsec (\frac{1}{2 3} x) + C

\frac{d}{d x} (cos (x) sec^{2} (x))

\int \frac{2 - x ^{2}}{( x ^{3} - 6 x + 1 ) ^{5}} d x

\int (3 x - 1)^{4} d x

\int_{0}^{1} \frac{37}{x ^{p}} d x

\frac{d}{d x} (e^{3 x^{2}} \cdot 6 x)

What is the integral of 1/(xsqrt(x^2-12)) ?
The integral of 1/(xsqrt(x^2-12)) is 1/(2sqrt(3))arcsec(1/(2sqrt(3))x)+C