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

The integral from-1 to 1 of 1/(1-x^2) is diverges

Popular >

integral from-1 to 1 of 1/(1-x^2)

\int_{- 1}^{1} \frac{1}{1 - x ^{2}} d x

diverges

Solution steps

\int_{- 1}^{1} \frac{1}{1 - x ^{2}} d x

Use the common integral:

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

= [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{- 1}^{1}

Simplify

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{- 1}^{1} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{- 1}^{1}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{- 1}^{1}

Compute the boundaries:

diverges

= diverges

\int_{50}^{100} \frac{x}{15 + 4 x ^{2}} d x

\int_{- 2}^{3} e^{u + 2} d u

\int_{0}^{3} 9 e^{3 x} d x

\int_{0}^{1} \frac{3}{2} (1 - x^{2}) d x

\int_{0}^{1} e^{- y^{2}} d y

What is the integral from-1 to 1 of 1/(1-x^2) ?
The integral from-1 to 1 of 1/(1-x^2) is diverges