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 Sep24 awarded Autobiographer Jul2 awarded Curious Dec5 awarded Yearling Oct12 asked What does $e^z,|z|=1$ look like？ Sep27 accepted How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? Sep26 accepted How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? Sep26 comment How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? As it is a trigonometry form. Is it a natural way to think the Euler formula? Sep26 comment How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? Great ! How does the ideal of using $I(a)$ or $ln（\frac{a+a^{-1}}{2}+cosx)$ come out? Sep26 revised How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? added 147 characters in body Sep26 revised How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? added 3 characters in body; edited title Sep26 asked How to evaluate $\int_{0}^{\pi} \log(2+\cos x)dx$? Sep26 accepted How to compute the number of Sylow p-subgroups of $GL_{n}(F_{p})$ ？ Sep26 revised How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? added 87 characters in body Sep25 comment How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? @experimentX The $pi$ is redundant. Sep25 revised How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? added 4 characters in body Sep25 comment How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? @experimentX How do you copmute the integration? Sep25 revised How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? edited title Sep25 asked How to prove $\lim_{n\to \infty} \prod_{i=0}^{n-1}$ $(2+\cos \frac{i \pi}{n})^{\frac{\pi}{n}}$=$\sqrt{3}$ by the sum form of a integration? Sep23 revised How to compute the number of Sylow p-subgroups of $GL_{n}(F_{p})$ ？ edited tags Sep23 comment How to compute the number of Sylow p-subgroups of $GL_{n}(F_{p})$ ？ Thanks.Is the explaination above a basic skill or common sense for matrix group(or linear group) problem ,or just for solving problems of linear algebra about the invariant space ? I have only learned some basic linear algebra for engineering. The method seems to depend on comprehension of linear space and how could a matrix be diagonalizable with its eigenvalues.