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

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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

y = 12 - x^{2}, y = - 4 x + 0, [3, 8]

\frac{d}{d x} (e^{1 + x})

\int sec (2 x) tan^{5} (2 x) d x

\int (e^{x y}) d y

(\frac{1}{tan ( x )})^{^{'}}

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