integral of xarctan(20x)

解答

\int x arctan (20 x) d x

\frac{1}{2} x^{2} arctan (20 x) - \frac{1}{800} (- arctan (20 x) + 20 x) + C

求解步骤

\int x arctan (20 x) d x

使用分布积分法

= \frac{1}{2} x^{2} arctan (20 x) - \int \frac{10 x ^{2}}{400 x ^{2} + 1} d x

\int \frac{10 x ^{2}}{400 x ^{2} + 1} d x = \frac{1}{800} (- arctan (20 x) + 20 x)

= \frac{1}{2} x^{2} arctan (20 x) - \frac{1}{800} (- arctan (20 x) + 20 x)

解答补常数

= \frac{1}{2} x^{2} arctan (20 x) - \frac{1}{800} (- arctan (20 x) + 20 x) + C

d er i v a t i v e \frac{x}{x ^{2} - 2}

\int (3 x^{2} + 5) cos (7 x) d x

d er i v a t i v e x^{7} \cdot e^{x}

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\frac{\partial}{\partial x} (x - \frac{1}{x} e^{\frac{y}{x}})