# azhi

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# 20 Questions

 8 How to estimate the limit $\lim_{x\to+\infty}\frac{\int_0^x|\sin(s)|ds}{x}?$ 6 How to compute this integral $\int_0^1 x^2 \arctan (e^{-x}) dx$ 5 how to estimate this indefinite integral $\int \frac{1}{e^x +x}dx$ 4 How to evaluate this definite integral $\int_0^2(1-x^2)^\frac{1}{3}~dx$ 4 how to proof the uniqueness of the subset of positive numbers

# 448 Reputation

 +10 how to estimate this indefinite integral $\int \frac{1}{e^x +x}dx$ +10 Is it possible to list $\mathbb{Q}$ so that the result set to be a monotonic sequence? +15 A summation identity which is for me hard to verify +5 Is there any quick method to solve this second-order semilinear ODE

 5 $\int_0^{\pi}{x \over{a^2\cos^2 x+b^2\sin^2 x}}dx$ 3 Linear homogenous ODE of second order 1 Finding volume of a figure given by relations. 1 Is there an easy way to expand $\arctan(1+x)$ at point $x=0$ 0 Check whether the three vectors $A(2,-1,2),B(1,2,-3),C(3,-4,7)$ are in the same plane

# 23 Tags

 7 calculus × 16 1 taylor-expansion × 2 5 integration × 5 0 limits × 6 5 definite-integrals × 2 0 real-analysis × 4 3 differential-equations × 2 0 pde × 3 1 volume × 2 0 fourier-analysis

# 8 Accounts

 Mathematics 448 rep 17 TeX - LaTeX 289 rep 17 MathOverflow 111 rep 4 Code Review 108 rep 2 English Language & Usage 106 rep