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

解答

\int \frac{ln ( x ^{2} - 1 )}{x ^{2}} d x

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

求解步骤

\int \frac{ln ( x ^{2} - 1 )}{x ^{2}} d x

使用分布积分法

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

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

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

化简

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

解答补常数

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

\int 1 + (\frac{e ^{x} - e ^{- x}}{2})^{2} d x

\int (7 x - 1) e^{2 x} d x

\int 0.04 x + 27 d x

\int x tan^{2} (x^{2}) sec^{2} (x^{2}) d x

in t e g r a l 3