1/(ax^2+b)dx 积分

题目

1/(ax^2+b)dx 积分

答案

补充楼上
∫dx/(ax^2+b)
=(1/b)∫dx/(1+ax^2/b)
a/b>0
=(1/b)∫dx/(1+(x√(a/b))^2)
=(1/b)√(b/a)∫d(x√(a/b))/(1+(x√(a/b)^2)
=(1/b)√(b/a)arctan[x√(a/b)] +C
a/b