来自廖浩燕的问题
请问一到数学题∫dx/(x^2-2x+3)^2=?
请问一到数学题∫dx/(x^2-2x+3)^2=?
1回答
2020-03-10 11:49
请问一到数学题∫dx/(x^2-2x+3)^2=?
请问一到数学题∫dx/(x^2-2x+3)^2=?
∫▒dx/(〖(x〗^2-2x+3)^2)
=∫▒dx/(((x-1)^2+2)^2)
=∫▒dx/(4*(〖(((x-1))/2)〗^2+1)^2)
令(x-1)/2=tan(t)
原式=∫▒〖√2/4cos^2(t)〗dt
=√2/16sin(2t)+√2/8t+c