What is the integral of 1/(xsqrt(25x^2-5)) ?

The integral of 1/(xsqrt(25x^2-5)) is 1/(sqrt(5))arcsec(sqrt(5)x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(xsqrt(25x^2-5))

\int \frac{1}{x 25 x ^{2} - 5} d x

\frac{1}{5} arcsec (5 x) + C

Solution steps

\int \frac{1}{x 25 x ^{2} - 5} d x

Apply Trigonometric Substitution

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

= \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{1}{5} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{5} \cdot 1 \cdot u

Substitute back

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

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

Simplify

\frac{1}{5} \cdot 1 \cdot arcsec (\frac{5}{5} x) : \frac{1}{5} arcsec (5 x)

= \frac{1}{5} arcsec (5 x)

Add a constant to the solution

= \frac{1}{5} arcsec (5 x) + C

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

\int (5 x^{3} + 7 x - 2) d x

\int x (x^{2} + 100)^{100} d x

\int \frac{6}{144 - 9 x ^{2}} d x

\int \frac{e ^{x}}{2 e ^{x} + 3} d x

What is the integral of 1/(xsqrt(25x^2-5)) ?
The integral of 1/(xsqrt(25x^2-5)) is 1/(sqrt(5))arcsec(sqrt(5)x)+C