What is the integral from 2 to 10 of 1/(1-x^2) ?

The integral from 2 to 10 of 1/(1-x^2) is (ln(11)-3ln(3))/2

Popular >

integral from 2 to 10 of 1/(1-x^2)

\int_{2}^{10} \frac{1}{1 - x ^{2}} d x

\frac{ln ( 11 ) - 3 ln ( 3 )}{2}

Decimal Notation

- 0.44897 \dots

Solution steps

\int_{2}^{10} \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}]_{2}^{10}

Simplify

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{2}^{10} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{2}^{10}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{2}^{10}

Compute the boundaries:

\frac{ln ( 11 ) - 3 ln ( 3 )}{2}

= \frac{ln ( 11 ) - 3 ln ( 3 )}{2}

\int_{2}^{x^{3}} ln (t^{2}) d t

\int_{- π}^{π} sin (2 x) cos (3 x) d x

\int_{0}^{π} cos (6 x) sin (5 x) d x

\int_{0}^{2} \frac{9}{5} x d x

\int_{0}^{20} 4 (400 - y^{2}) d y

What is the integral from 2 to 10 of 1/(1-x^2) ?
The integral from 2 to 10 of 1/(1-x^2) is (ln(11)-3ln(3))/2