integral of ln^2(2/x)

解答

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

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

求解步骤

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

使用分布积分法

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

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

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

化简

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

解答补常数

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

\int \frac{x ^{3} + 4 x ^{2} + 7 x + 6}{x ^{2} + 3 x + 4} d x

\int (2 x^{5} + 5 x^{4} + 2 x^{3} - \frac{3}{x ^{2}} + 4) d x

\int \frac{y ^{2} + 12 y + 36}{( y ^{2} + 36 ) ^{2}} d y

\int x^{2} - 4 x - 77 d x

\int x^{3} + \frac{1}{x} + 1 + 2 x d x