What is the integral of 1/(xsqrt(4-(ln(x))^2)) ?

The integral of 1/(xsqrt(4-(ln(x))^2)) is arcsin(1/2 ln(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(xsqrt(4-(ln(x))^2))

\int \frac{1}{x 4 - ( ln ( x ) ) ^{2}} d x

arcsin (\frac{1}{2} ln (x)) + C

Solution steps

\int \frac{1}{x 4 - ( ln ( x ) ) ^{2}} d x

Simplify

= \int \frac{1}{x 4 - ln ^{2} ( x )} d x

Apply u-substitution

= \int \frac{1}{4 - u ^{2}} d u

Apply Trigonometric Substitution

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

= 1 \cdot arcsin (\frac{1}{2} ln (x))

Simplify

= arcsin (\frac{1}{2} ln (x))

Add a constant to the solution

= arcsin (\frac{1}{2} ln (x)) + C

What is the integral of 1/(xsqrt(4-(ln(x))^2)) ?
The integral of 1/(xsqrt(4-(ln(x))^2)) is arcsin(1/2 ln(x))+C