Question

高数题 ∫上-2下-3 dx/x²乘以根号下（x²-1） 令x= 1/t

Answer 1

令x=1/t,则dx=-dt/t^2；x∈[-3,-2],t∈[-1/3,-1/2]；

∴∫（-3,-2）dx/x^2√(x^2-1)=∫(-1/3,-1/2)(-dt/t^2)t^2*t/√(1-t^2)

=∫(-1/3,-1/2)(1/2)d(1-t^2)/√(1-t^2)

=√(1-t^2)I(-1/3,-1/2)

=√[1-(-1/2)^2]-√[1-(-1/3)^2

=(3√3-4√2)/6