Цитата(tig81 @ 11.4.2009, 22:54) *

Например, intdt/(2-t^2)=(1/2)intdt/(1-t^2/2)=(1/2)intdt/(1-[t/sqrt(2)]^2)=...



1) int[sqrt(x)dx/(4-x)] = |x=t^2| = int[2t^2dt/(4-t^2)] = int[-2+8/(4-t^2)dt] = int[-2+8/(4-t^2)dt] = int[-2dt]+int[8dt/(4-t^2)] = int[-2dt]+1/2int[8dt/((2-t^2)/2)] = int[-2dt]+1/2int[8dt/((2-t^2)/2)] = int[-2dt]+1/4int[8dt/((1-t^2)/4)] = int[-2dt]+1/4int[8dt/((1-(t/4)^2] = -2t+2ln(1-t/4)(1+t/4)+C, так?

3) int[sqrt(x+2)dx/x) = | x+2 = t^2| = int[2t^2dt/(t^2-2)] = int[2+4/(t^2-2)dt] = int[2dt]+int[4/(t^2-2)dt] = int[2dt]-int[4/(2-t^2)dt] = int[2dt]-1/2int[4/(1-t^2/2)dt] = int[2dt]-1/2int[4/(1-(t/2)^2dt] = 2t-2ln(1-t/2)(1+t/2)+C, a здесь?