integral from 2 to 6 of t^2ln(2t)

解答

\int_{2}^{6} t^{2} ln (2 t) d t

72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

十进制

152.10538 \dots

求解步骤

\int_{2}^{6} t^{2} ln (2 t) d t

使用分布积分法

= [\frac{1}{3} t^{3} ln (2 t) - \int \frac{t ^{2}}{3} d t]_{2}^{6}

\int \frac{t ^{2}}{3} d t = \frac{t ^{3}}{9}

= [\frac{1}{3} t^{3} ln (2 t) - \frac{t ^{3}}{9}]_{2}^{6}

带入上下限计算后得:

72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

= 72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

d er i v a t i v e - 6 3 x^{2}

d er i v a t i v e (x)^{2}

\frac{\partial}{\partial y} (y + x)

a re a y = \frac{1}{( 9 x ^{3} )}, 1, 100

20 y^{^{''}} + 4 y^{^{'}} + y = 0