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Solve ∫ (from 0 to 1) of sqrt {1+x^4 wrt x | Microsoft Math Solver Integral involving Square roots of polynomials: ∫ 01 1+xa dx? We have I=\int_0^1\sqrt {1+x^a}\,\mathrm dx=\int_0^1\sum_ {k=0}^\infty\binom {1 2} {k}x^ {ka}\mathrm dx, where \binom {1 2} {k}=\frac { (1 2) (1 2-1)\dots (1 2-k+1)} {k!} We get I=\sum_ {k=0}^\infty\binom {1 2} {k}\frac1 {1+ka}=\sum_ {k=0}^\infty
Estimate $\\int_0^{\\infty} 1 \\sqrt{1+x^4} \\mathrm{d}x$ I need an analytical estimation of the following integral: $$\int\limits_0^\infty \frac { {\mathrm {d} x}} {\sqrt {1 + x^4}}$$ It has a root in the denomenator -- so I can't make use of complex residues