微积分

集成技术

使用代换 $\ ln x = t)$ 下面哪个选项等于 $\int_{e}^{e^{6}} \frac{3(\ln x)^2}{x} dx ?$

\int_{1}^{6}3t ^2e^t dt

\int_{0}^{6} 3t ^2 dt

\int_{0}^{6} \frac{3t ^2}{e^t} dt

\int_{1}^{6}3t ^2 dt

评估 $\ displaystyle {\ int_0 ^{3} \压裂{12 x + 6} {x ^ 2 + x + 1} dx。}$

\压裂{10}{39}

\压裂{1}{13}

{6} (\ ln {13} - \ ln {3})

{6} \ ln {13}

使用代换 $u = \ sin (x),$ 评估 $\ displaystyle {\ int_0 ^ \压裂{\π}{2}\罪^ {10}x \因为新。}$

\压裂{\π}{11}

\压裂{\π}{10}

\压裂{1}{11}

\压裂{1}{10}

评估 $\ displaystyle {\ int_0 ^ \压裂{\π}{32}3 \ tan8xdx。}$

\压裂{3}{16}\ ln3

- - - - - - \压裂{3}{16}\ ln3

\压裂{3}{16}\ ln2

- - - - - - \压裂{3}{16}\ ln2

使用代换 $u = e ^ {x ^ 2},$ 评估 $\ displaystyle {\ int_0 ^ {3} 12 x e ^ {x ^ 2} dx。}$

{6} (e ^ {9} 1)

{12} e ^ {3}

{12} (e ^ {3} 1)

{6} e ^ {9}