integral of x^3ln(x^3)

解答

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

\frac{3}{4} x^{4} ln (x) - \frac{3 x ^{4}}{16} + C

求解步骤

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

使用分布积分法

= \frac{1}{4} x^{4} ln (x^{3}) - \int \frac{3 x ^{3}}{4} d x

\int \frac{3 x ^{3}}{4} d x = \frac{3 x ^{4}}{16}

= \frac{1}{4} x^{4} ln (x^{3}) - \frac{3 x ^{4}}{16}

\frac{1}{4} x^{4} ln (x^{3}) = \frac{3}{4} x^{4} ln (x)

= \frac{3}{4} x^{4} ln (x) - \frac{3 x ^{4}}{16}

解答补常数

= \frac{3}{4} x^{4} ln (x) - \frac{3 x ^{4}}{16} + C

y^{^{'}} = \frac{1}{sec ^{2} ( y )}

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 3 x )})

x \to 2 lim (e^{2 x - x^{2}})

\int y e^{z} d z

\int \frac{x ^{4} + 1}{x ^{3}} d x