The same trick can be used to solve many intimidating looking integrals like:-
i) Integral 5 sin\^4(x\^2)/x\^6 - 8 cos(x\^2) sin\^3(x\^2)/x\^4
Ans:- (-)sin\^4(x\^2)/(x\^5), Note:- we have f(x\^2) here instead of f(x) so need to account 2x as derivative of x\^2 due to chain rule
ii) Integral tan\^2 (x)/x\^5- 4 ln(x) tan\^2 (x)/x\^5 + 2 tan(x) ln(x)/(x\^4) + 2 ln(x) tan\^3 (x)/x\^4
Ans:- tan\^2(x)ln(x)/x\^4