题目
26. (3.0分) int (2x+1)^10dx= (1)/((2x+1)^11)+C
26. (3.0分) $\int (2x+1)^{10}dx=$ $\frac{1}{(2x+1)^{11}+C}$
题目解答
答案
设 $u = 2x + 1$，则 $du = 2dx$，即 $dx = \frac{1}{2}du$。代入原积分得：
\[
\int (2x+1)^{10}dx = \int u^{10} \cdot \frac{1}{2}du = \frac{1}{2} \int u^{10}du = \frac{1}{2} \cdot \frac{u^{11}}{11} + C = \frac{u^{11}}{22} + C
\]
将 $u = 2x + 1$ 代回，得：
\[
\boxed{\frac{(2x+1)^{11}}{22} + C}
\]