Recent content by kamke

∫...dx = 1/2 *(lnlnx - ln((2*(lnx*lnx + 2*lnx + 4)^(1/2) + lnx + 4)) + C

|x| + |y| ≥ √(x*x +y*y) / ( )2 squaring x*x + y*y + 2*|x*y| ≥ x*x + y*y /-x*x,-y*y 2*|x*y| ≥ 0 /:2 |x*y| ≥ 0 It is true. |x*y| = 0 ↔ x = 0 or y = 0 kamke

for example (x*x+1)*(x*x+2)*(x*x+3)*(x*x+4) = x^8 + a*x^6 + b*x^4 + c*x^2 + 1*2*3*4 1*2*3*4 = 4! (x*x+1)*(x*x+2)*(x*x+3)*(x*x+4) = x^8 + 10x^6 + 35x^4 + 50x^2 + 24 Each member must be integrated. ∫ x^8 + 10x^6 + 35x^4 + 50x^2 + 24 dx = = x^9/9 + 10x^7/7 + 7x^5 +50x^3/3...

Dear Bigfooted, Thanks. Erich Kamke (1890-1961) German mathematician u'' = x^(1-n)*u^n n = 2 u'' = x^(-1)*u^2 u(x) = 2/x (+ u ≡ 0) I take great interest in implicit solution. kamke

Hi, Prudnikov: Integrals and series ∫(x,∞) e^(-ax)/x dx = -Ei(-ax) a>0 Ei(x) = ∫(-∞,x) e^t/t dt is the exponential integral Bronstejn Ei(x) = ∫(-∞,x) e^t/dt = C + ln|x| + x + x*x/(2*2!) + ... + x^n/(n*n!) + ... C = 0.577215665 kamke

Hi, y'' = y^2/x y(x) = ? Trial and error: y(x) = 2/x. I am glad to get a particular solution too. Thanks, kamke