Đáp án:
$\dfrac{1}{12}(x+1)^{12} -\dfrac{1}{11}(x +1)^{11} + C\quad$ (C: hằng số)
Giải thích các bước giải:
$\quad \displaystyle\int x(x+1)^{10}dx$
Đặt $u = x+1\longrightarrow x = u -1$
$\to du = dx$
Ta được:
$\quad \displaystyle\int(u-1).u^{10}du$
$= \displaystyle\int(u^{11} - u^{10})du$
$=\displaystyle\int u^{11}du - \displaystyle\int u^{10}du$
$= \dfrac{u^{12}}{12} -\dfrac{u^{11}}{11} + C$
$=\dfrac{1}{12}(x+1)^{12} -\dfrac{1}{11}(x +1)^{11} + C\quad$ (C: hằng số)
