∫[(x+2)/(x^2+2x+3)]dx

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/09/24 01:19:34

∫[(x+2)/(x^2+2x+3)]dx
∫(dx)/(1+e^x) 感激不尽!
x^2+2x+3怎么等于(x+1)(x+2)啊？……

∫[(x+2)/(x^2+2x+3)]dx=1/2∫[(2x+4)/(x^2+2x+3)]dx
=1/2∫[(2x+2+2)/(x^2+2x+3)]dx
=1/2[∫(2x+2)/(x^2+2x+3)dx+∫2/(x^2+2x+3)]dx
=1/2[∫1/(x^2+2x+3)d(x^2+2x+3)+2∫1/(x^2+2x+3)dx]
=1/2[ln(x^2+2x+3)+√2arctan(2x+2)/(2√2)+C]

∫[(x^2-x+6)/(x^3+3x)]dx ∫2^x*3^x/(9^x-4^x) dx ∫(2^x)/((2^x)+3)dx ∫(1-x)^2/x^3 dx ∫(x-1)^2/x^3 dx ∫x^3/1+x^2 dx ∫(X^3)/(1+X^2)dx ∫X^2 e^-X^3 dx. ∫x^3/9+X^2 dx. ∫x^3/(9+x^2)dx ∫(2^x+3^x)²dx x-9/[(根号)x]+3 dx ∫ x+1/[(根号)x] dx ∫ [（3-x^2）]^2 dx