Question

一道超难的数学题(对于我来说)

求一个函数f(x),使其微分等于dx/{x[cos(lnx)]^2} 看明白题目了吗,进来指教指教啊

Answer 1

f(x)=∫dx/{x[cos(lnx)]^2}
设：t=lnx, x=e^t. dx=e^t/dt
f(x)=∫dx/{x[cos(lnx)]^2}
=∫e^tdt/{e^t[cos(t)]^2}
=∫dt/{[cos(t)]^2}
=tgt+c
=tg(lnx)+c