计算∫1⼀[x(2x^2-1)^1⼀2]dx

2025-06-26 05:46:10
推荐回答(2个)
回答1:

原函数=∫(1/√2)/[x^2(1-1/(√2x)^2)^(1/2)dx,1/√2x=cost,x=1/(√2cost),dx=(1/√2)sint/(cost)^2dt
原函数=∫((cost)^2/sint)(sint/(cost)^2)dt=t+C,t=arccos(1/√2x)
原函数=arccos(1/√2x)+C

回答2:

log(((2*x^2 - 1)^(1/2) + i)/x)*i