What is the integral of (sqrt(5))/(xsqrt(4-ln^2(x))) ?

The integral of (sqrt(5))/(xsqrt(4-ln^2(x))) is sqrt(5)arcsin(1/2 ln(x))+C

Popular >

integral of (sqrt(5))/(xsqrt(4-ln^2(x)))

\int \frac{5}{x 4 - ln ^{2} ( x )} d x

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

Solution steps

\int \frac{5}{x 4 - ln ^{2} ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{1}{x 4 - ln ^{2} ( x )} d x

Apply u-substitution

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

= 5 \cdot \int \frac{1}{4 - u ^{2}} d u

Apply Trigonometric Substitution

: \int 1 d v

= 5 \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= 5 \cdot 1 \cdot v

Substitute back

= 5 \cdot 1 \cdot arcsin (\frac{1}{2} ln (x))

Simplify

= 5 arcsin (\frac{1}{2} ln (x))

Add a constant to the solution

= 5 arcsin (\frac{1}{2} ln (x)) + C

\frac{d}{d x} (- 12 x cos (x^{2}) + 8 x^{3} sin (x^{2}))

\frac{d}{d x} (12 x^{3} - 48 x^{2} + 48 x)

\frac{1}{s ^{2} + 6 s + 13}

\int \frac{x ^{2} + 49}{x} d x

f (x) = x - 4

What is the integral of (sqrt(5))/(xsqrt(4-ln^2(x))) ?
The integral of (sqrt(5))/(xsqrt(4-ln^2(x))) is sqrt(5)arcsin(1/2 ln(x))+C