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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

integral

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

\frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + C

Solution steps

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

Apply Integral Substitution

= \int \frac{1}{2 ( - u ^{2} + 1 )} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{- u ^{2} + 1} d u = \frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}

= \frac{1}{2} (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2})

Substitute back

u = \frac{x}{2}

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

Simplify

\frac{1}{2} (\frac{ln \frac{x}{2} + 1}{2} - \frac{ln \frac{x}{2} - 1}{2}) : \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1)

= \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1)

Add a constant to the solution

= \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + C

\frac{1}{( x ^{2} + x + 1 )}

\frac{sin ^{2} ( x )}{cos ^{2} ( x )}

cos^{3} (x) - cos (x)

\frac{x ^{2}}{3}

sin (2 - 4 x)

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