user149844

 36 A Putnam Integral $\int_2^4 \frac{\sqrt{\ln(9-x)}\,dx}{\sqrt{\ln(9-x)} + \sqrt{\ln(x+3)}}.$ 10 Evaluation of $\int\frac{5x^3+3x-1}{(x^3+3x+1)^3}\,dx$ 7 Integrating $\int \frac{1}{\sqrt[4]{1+x^4}} dx$ 5 Integrate $\int\frac{\cos^2x}{1+\tan x}dx$ 3 Find $\int \frac{x^2}{(x \cos x - \sin x)(x \sin x + \cos x)}dx$

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### Questions (6)

 4 Is this proof correct? Divergence of $\int_{1}^{\infty} \left| \frac{\sin x}{x} \right| \, \mathrm{d}x$ 3 Apostol's proof of Arzelà's Bounded Convergence Theorem 3 How can I show that the integral equals zero? 2 Proving that $\prod_{i=1}^{n} (1 + a_{i}) \ge \left(1 + \prod_{i=1}^{n} a_{i}^{1/n} \right)^{n}$ [duplicate] 2 Functions disagreeing on a set of measure zero - Proof verification

### Tags (21)

 80 integration × 22 3 convergence × 3 58 calculus × 23 3 divergent-series × 2 36 contest-math 2 improper-integrals × 4 22 indefinite-integrals × 9 2 trigonometry 3 sequences-and-series × 4 0 real-analysis × 4