integral of x^2sqrt(2-x)

解答

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

\frac{2}{7} x^{3} - x + 2 - \frac{4}{35} x^{2} - x + 2 - \frac{32}{105} x - x + 2 - \frac{128}{105} - x + 2 + C

求解步骤

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

使用分布积分法

= \frac{1}{3} x^{3} 2 - x - \int - \frac{x ^{3}}{6 2 - x} d x

\int - \frac{x ^{3}}{6 2 - x} d x = \frac{1}{105} (5 x^{3} + 12 x^{2} + 32 x + 128) - x + 2

= \frac{1}{3} x^{3} 2 - x - \frac{1}{105} (5 x^{3} + 12 x^{2} + 32 x + 128) - x + 2

化简

\frac{1}{3} x^{3} 2 - x - \frac{1}{105} (5 x^{3} + 12 x^{2} + 32 x + 128) - x + 2 : \frac{2}{7} x^{3} - x + 2 - \frac{4}{35} x^{2} - x + 2 - \frac{32}{105} x - x + 2 - \frac{128}{105} - x + 2

= \frac{2}{7} x^{3} - x + 2 - \frac{4}{35} x^{2} - x + 2 - \frac{32}{105} x - x + 2 - \frac{128}{105} - x + 2

解答补常数

= \frac{2}{7} x^{3} - x + 2 - \frac{4}{35} x^{2} - x + 2 - \frac{32}{105} x - x + 2 - \frac{128}{105} - x + 2 + C

d er i v a t i v e f (x) = \frac{x ( x ^{2} + 4 )}{x - 2}

\int 7 x^{- \frac{8}{9}} d x

\frac{y ^{^{'}}}{x ^{3} + y} = \frac{1}{x}

\int \frac{co tan ( ln ( x ) )}{2 x}

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