# user1043065

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# 13 Questions

 5 How do I write this proof down? 4 How do I evaluate the integral $\int_0^{\infty}\frac{x^5\sin(x)}{(1+x^2)^3}dx$? 4 Show that $g\in\mathcal{L}^q(\mu)$. 3 Prove that $e^{\ln{z}}=z$ from the power series 3 Prove combinatorics problem $\sum_{k=0}^n {2k \choose k}{2n-2k \choose n-k}=4^n$ using generating functions

# 396 Reputation

 +20 How do I evaluate the integral $\int_0^{\infty}\frac{x^5\sin(x)}{(1+x^2)^3}dx$? +10 Prove that a group of order 30 has at least three different normal subgroups +10 Prove that periodic analytic function can be written as $\sum_{-\infty}^{\infty} c_n e^{2\pi inz}$ +10 A small airplane is flying due north at $150\,\rm km/h$ when it encounters a wind of $80\,\rm km/h$ from the east.

 5 Why sin and cos do not get the same result that as tan, in this case? 2 A small airplane is flying due north at $150\,\rm km/h$ when it encounters a wind of $80\,\rm km/h$ from the east. 1 Prove that a group of order 30 has at least three different normal subgroups 1 Probability exercise (archers) 0 How to prove the uniqueness of a polynomial with such properties?

# 31 Tags

 5 trigonometry 1 probability 2 calculus × 3 1 group-theory 2 vectors 0 integration × 4 1 abstract-algebra 0 elementary-set-theory × 3 1 sylow-theory 0 complex-analysis × 3

# 7 Accounts

 Mathematics 396 rep 18 Stack Overflow 137 rep 6 Drupal Answers 111 rep 1 Physics 106 rep 2 Super User 101 rep