第1个回答 2011-11-28
1/2(tgx)^2+ln|cosx|+C.
第2个回答 2011-11-28
是不是要求积分？
∫(tan(x))^3 dx=∫(sin(x))^3/(cos(x))^3 dx = ∫(1-(cos(x))^2)sin(x)/(cos(x))^3 dx
=∫((cos(x))^2-1)/(cos(x))^3 d(cos(x))
设cos(x)=t,原式=∫(t^2-1)/t^3 dt=∫1/t dt-∫t^(-3) dt=ln(t)+1/2*t(-2)+c(c为常数)
=ln(cos(x))+1/(2(cos(x))^2)+c(c为常数)本回答被提问者采纳
∫(tan(x))^3 dx=∫(sin(x))^3/(cos(x))^3 dx = ∫(1-(cos(x))^2)sin(x)/(cos(x))^3 dx
=∫((cos(x))^2-1)/(cos(x))^3 d(cos(x))
设cos(x)=t,原式=∫(t^2-1)/t^3 dt=∫1/t dt-∫t^(-3) dt=ln(t)+1/2*t(-2)+c(c为常数)
=ln(cos(x))+1/(2(cos(x))^2)+c(c为常数)本回答被提问者采纳
相似回答
