What is the integral of 1/(tsqrt(1-ln^2(t))) ?

The integral of 1/(tsqrt(1-ln^2(t))) is arcsin(ln(t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(tsqrt(1-ln^2(t)))

\int \frac{1}{t 1 - ln ^{2} ( t )} d t

arcsin (ln (t)) + C

Solution steps

\int \frac{1}{t 1 - ln ^{2} ( t )} d t

Apply u-substitution

= \int \frac{1}{1 - u ^{2}} d u

Use the common integral:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= arcsin (u)

Substitute back

u = ln (t)

= arcsin (ln (t))

Add a constant to the solution

= arcsin (ln (t)) + C

What is the integral of 1/(tsqrt(1-ln^2(t))) ?
The integral of 1/(tsqrt(1-ln^2(t))) is arcsin(ln(t))+C