求不定积分∫3t·根号下开三次方[2(t^2)-1

求不定积分∫3t·根号下开三次方[2(t^2)-1] dt

2个回答

∫3t·³√(2t²-1) dt
=3∫t·³√(2t²-1) dt
=3/4·∫³√(2t²-1) d(2t²-1)
=3/4×3/4×(2t²-1)^(3/4)+C
=9/16·(2t²-1)^(3/4)+C