integral from 7/6 to 6 of 1/(1-x^2)

解答

\int_{\frac{7}{6}}^{6} \frac{1}{1 - x ^{2}} d x

\frac{ln ( 7 ) - ln ( 65 )}{2}

十进制

- 1.11423 \dots

求解步骤

\int_{\frac{7}{6}}^{6} \frac{1}{1 - x ^{2}} d x

使用积分常见定则:

\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}]_{\frac{7}{6}}^{6}

化简

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{\frac{7}{6}}^{6} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{7}{6}}^{6}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{\frac{7}{6}}^{6}

带入上下限计算后得:

\frac{ln ( 7 ) - ln ( 5 ) - ln ( \frac{13}{6} ) - ln ( 6 )}{2}

= \frac{ln ( 7 ) - ln ( 5 ) - ln ( \frac{13}{6} ) - ln ( 6 )}{2}

化简

= \frac{ln ( 7 ) - ln ( 65 )}{2}

d er i v a t i v e 9 x^{2} cos (x) cot (x)

t an g e n t f (x) = \frac{7}{x}, (4, \frac{7}{2})

\frac{d y}{d x} - 2 y = e^{5 x}

\frac{d}{d x} (- 5 sin (2 x))

\frac{d}{d x} (cos (x + 1))