1 Recursive relation induction problem: $c_n = \frac{1}{2^n} \cdot \sum_{k \text{ even}}^{0~ \leq ~k~ \leq ~n} {n \choose k}c_k$ 1 How to integrate $\int \frac{x}{\sqrt{x^4+10x^2-96x-71}}dx$? 1 Integral $\int \frac{2x^2-1}{\pm x(2x^2-1)+2x+ \sqrt{1+2x^2}} d x$ 1 Examples of $C^1(\mathbb{R}^2)$ functions where mixed partials are equal nowhere 1 Does the converse of the chain rule hold in general?

### Reputation (184)

 +10 How to integrate $\int \frac{x}{\sqrt{x^4+10x^2-96x-71}}dx$? +25 Recursive relation induction problem: $c_n = \frac{1}{2^n} \cdot \sum_{k \text{ even}}^{0~ \leq ~k~ \leq ~n} {n \choose k}c_k$ +10 Integral $\int \frac{2x^2-1}{\pm x(2x^2-1)+2x+ \sqrt{1+2x^2}} d x$ +10 How to apply Risch's algorithm to $\int\frac{x}{\sqrt{x^4-2x^3+3x^2+4x+1}}\,\mathrm{d}x$?

### Questions (4)

 4 How to apply Risch's algorithm to $\int\frac{x}{\sqrt{x^4-2x^3+3x^2+4x+1}}\,\mathrm{d}x$? 3 Each Player Removes a Number and All Its Divisors 2 Sum of reciprocals of product of iterated logarithms 2 Stronger version of equality of mixed partials

### Tags (22)

 3 real-analysis × 6 1 algorithms × 2 3 calculus × 5 1 induction 2 multivariable-calculus × 4 1 elliptic-integrals 2 integration × 3 1 chain-rule 1 indefinite-integrals × 2 1 recurrence-relations

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