∫(x+1)/(x^2-2x+5)dx

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/25 18:22:50

∫(x+1)/(x^2-2x+5)dx

∫(x+1)/(x^2-2x+5)dx
=1/2*∫(2x-2)/(x^2-2x+5)dx+∫2/(x^2-2x+5)dx
=1/2*∫[1/(x^2-2x+5)]d(x^2-2x+5)+2∫1/[(x-1)^2+2^2])d(x-1)
=1/2*ln(x^2-2x+5)+arctan[(x-1)/2]+C

∫(x+1)/(x^2-2x+5)dx ∫[（x+1)/(x^(2)+2x+5]dx ∫X^2/1-x^2 dx. ∫dx/x^2(1-x^2) ∫dx/x^2(1+x^2) ∫1/(x^2+x+1)dx ∫x/（x^2+5）dx ∫（x^2+1/x^4)dx ∫(1-x)^2/x^3 dx ∫ x/(1+X^2)dx= ∫2 -1|x²-x|dx ∫(x-1)^2/x^3 dx