en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply u-substitution

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

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

Apply Trigonometric Substitution

: \int 1 d v

= \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

Popular Examples

integral of (4x^2+1)^2

\int (4 x^{2} + 1)^{2} d x

integral of sin(4x)cos^3(4x)

\int sin (4 x) cos^{3} (4 x) d x

integral of ((arctan(7x)))/(1+49x^2)

\int \frac{( arctan ( 7 x ) )}{1 + 49 x ^{2}} d x

integral of (xln(1+x^2))/(sqrt(1+x^2))

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

integral of (2/3)^x

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

Frequently Asked Questions (FAQ)

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