integral of (2x-5x^2)(2-10x)

解答

\int (2 x - 5 x^{2}) (2 - 10 x) d x

\frac{50 x ^{4}}{3} - \frac{25 x ^{4}}{6} - 10 x^{3} + 2 x^{2} + C

求解步骤

\int (2 x - 5 x^{2}) (2 - 10 x) d x

使用分布积分法

= (2 - 10 x) (x^{2} - \frac{5 x ^{3}}{3}) - \int - 10 (x^{2} - \frac{5 x ^{3}}{3}) d x

\int - 10 (x^{2} - \frac{5 x ^{3}}{3}) d x = - 10 (\frac{x ^{3}}{3} - \frac{5 x ^{4}}{12})

= (2 - 10 x) (x^{2} - \frac{5 x ^{3}}{3}) - (- 10 (\frac{x ^{3}}{3} - \frac{5 x ^{4}}{12}))

化简

(2 - 10 x) (x^{2} - \frac{5 x ^{3}}{3}) - (- 10 (\frac{x ^{3}}{3} - \frac{5 x ^{4}}{12})) : \frac{50 x ^{4}}{3} - \frac{25 x ^{4}}{6} - 10 x^{3} + 2 x^{2}

= \frac{50 x ^{4}}{3} - \frac{25 x ^{4}}{6} - 10 x^{3} + 2 x^{2}

解答补常数

= \frac{50 x ^{4}}{3} - \frac{25 x ^{4}}{6} - 10 x^{3} + 2 x^{2} + C

\int \frac{x + 1}{2 x ^{2} - 6 x + 4} d x

\frac{d}{d x} (2 π (\frac{x}{9.8})^{\frac{1}{2}})

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\frac{d y}{d x} + (x^{2}) y = 2 x^{2}