What is the integral of 1/(xsqrt(9x^2-7)) ?

The integral of 1/(xsqrt(9x^2-7)) is 1/(sqrt(7))arcsec(3/(sqrt(7))x)+C

Popular >

integral of 1/(xsqrt(9x^2-7))

\int \frac{1}{x 9 x ^{2} - 7} d x

\frac{1}{7} arcsec (\frac{3}{7} x) + C

Solution steps

\int \frac{1}{x 9 x ^{2} - 7} d x

Apply Trigonometric Substitution

: \int \frac{1}{7} d u

= \int \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{7} \cdot 1 \cdot u

Substitute back

u = arcsec (\frac{3}{7} x)

= \frac{1}{7} \cdot 1 \cdot arcsec (\frac{3}{7} x)

Simplify

= \frac{1}{7} arcsec (\frac{3}{7} x)

Add a constant to the solution

= \frac{1}{7} arcsec (\frac{3}{7} x) + C

x \to 3 lim (x^{2} + 2)

\int 3 b y^{2} d y

\frac{d}{d x} (\frac{1}{ln ( x - 1 )})

\int x^{2} 3 + 7 x^{2} d x

\frac{d}{d x} (ln (y - x^{2}))

What is the integral of 1/(xsqrt(9x^2-7)) ?
The integral of 1/(xsqrt(9x^2-7)) is 1/(sqrt(7))arcsec(3/(sqrt(7))x)+C