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Question Number 166182 by SANOGO last updated on 14/Feb/22
calculerlaprimitivede∫t2(1+t2)2dt
Answered by greogoury55 last updated on 14/Feb/22
t=tanuY=∫tan2u(1+tan2u)2sec2uduY=∫tan2usec4usec2uduY=∫tan2usec2udu=∫sin2uduY=∫1−cos2u2du=u−12sin2u2+cY=12arctan(t)−t2t2+2+c
Commented by SANOGO last updated on 14/Feb/22
merci
Answered by MJS_new last updated on 15/Feb/22
∫t2(t2+1)2dt=[Ostrogradski′sMethod]=−t2(t2+1)+12∫dtt2+1==−t2(t2+1)+12arctant+C
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