integral of xln^3(x)

解答

\int x ln^{3} (x) d x

\frac{1}{2} x^{2} ln^{3} (x) - \frac{3}{8} (2 x^{2} ln^{2} (x) - 2 x^{2} ln (x) + x^{2}) + C

求解步骤

\int x ln^{3} (x) d x

使用分布积分法

= \frac{1}{2} x^{2} ln^{3} (x) - \int \frac{3}{2} x ln^{2} (x) d x

\int \frac{3}{2} x ln^{2} (x) d x = \frac{3}{8} (2 x^{2} ln^{2} (x) - 2 x^{2} ln (x) + x^{2})

= \frac{1}{2} x^{2} ln^{3} (x) - \frac{3}{8} (2 x^{2} ln^{2} (x) - 2 x^{2} ln (x) + x^{2})

解答补常数

= \frac{1}{2} x^{2} ln^{3} (x) - \frac{3}{8} (2 x^{2} ln^{2} (x) - 2 x^{2} ln (x) + x^{2}) + C

\int_{0}^{2} \frac{1}{4 + x ^{2}} d x

\frac{d}{d x} (a x)

n = 1 \sum \infty n sin (nπ)

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

\frac{\partial}{\partial x} (3 x^{2} - y^{3} + x - 1)