∫cos^2 3tdt
=∫（1+cos6t）/2dt
=∫1/2+cos6t/2dt
=1/2t+1/12sin6t+C
∫dx/sinxcosx
=∫2(dx)/[2sinxcosx]
=∫[2dx]/[tanxcos²x]
=2∫[dtanx]/tanx
=2ln│tanx│+C
另一种方法是
2∫cscx dx=2ln│cscx-cotx│+C
3.∫dx/e^2x+e^-2x
令e^x=t,则x=lnt.带入化得
∫t^3/t^4+1dx
=1/4*ln(t^4+1)
则∫dx/e^2x+e^-2x
=1/4*ln(e^4x+1)
4.∫x/1+2x^4 dx
=1/(2√2)*arctan(√2x^2)+C