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

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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

= \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

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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