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

解答

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

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

求解步骤

\int \frac{x ^{2}}{2 x - x ^{2}} d x

使用分布积分法

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

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

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

解答补常数

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

\int e^{s i n (2 θ)} cos (2 θ) d θ

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

\int sin (6 x) sin (4 x) d x

\int (4 x^{\frac{1}{3}} + 6 x^{- 7} + 10) d x

\int \frac{1}{x ^{2} 25 x ^{2} + 4} d x