What is the integral of-6/(7xsqrt(49x^2-25)) ?

The integral of-6/(7xsqrt(49x^2-25)) is -6/35 arcsec(7/5 x)+C

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integral of-6/(7xsqrt(49x^2-25))

\int - \frac{6}{7 x 49 x ^{2} - 25} d x

- \frac{6}{35} arcsec (\frac{7}{5} x) + C

Solution steps

\int - \frac{6}{7 x 49 x ^{2} - 25} d x

Take the constant out:

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

= - \frac{6}{7} \cdot \int \frac{1}{x 49 x ^{2} - 25} d x

Apply Trigonometric Substitution

: \int \frac{1}{5} d u

= - \frac{6}{7} \cdot \int \frac{1}{5} d u

Take the constant out:

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

= - \frac{6}{7} \cdot \frac{1}{5} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= - \frac{6}{7} \cdot \frac{1}{5} \cdot 1 \cdot u

Substitute back

u = arcsec (\frac{7}{5} x)

= - \frac{6}{7} \cdot \frac{1}{5} \cdot 1 \cdot arcsec (\frac{7}{5} x)

Simplify

- \frac{6}{7} \cdot \frac{1}{5} \cdot 1 \cdot arcsec (\frac{7}{5} x) : - \frac{6}{35} arcsec (\frac{7}{5} x)

= - \frac{6}{35} arcsec (\frac{7}{5} x)

Add a constant to the solution

= - \frac{6}{35} arcsec (\frac{7}{5} x) + C

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What is the integral of-6/(7xsqrt(49x^2-25)) ?
The integral of-6/(7xsqrt(49x^2-25)) is -6/35 arcsec(7/5 x)+C