Solution
= Solution
The fifth power of the <odd> function $\tanh x$ is odd and continuous. Its integral over the symmetric interval is therefore $\boxed{\int_{-1000}^{1000}\tanh^5x\,dx=0}$.
= Solution
The fifth power of the <odd> function $\tanh x$ is odd and continuous. Its integral over the symmetric interval is therefore $\boxed{\int_{-1000}^{1000}\tanh^5x\,dx=0}$.