PCSI2 — Interrogation de calcul du 18/3/2008 : les r´eponses
D.L. Equation Int´egrale SdR trigo
A x−5x2+ 29x3/6 2,−4−4i,4−3i 2 ln(2)/5−ln(5)/10 + arctan(1/2)10 1/2 −1/2 B −2x−2x2−4x3/3 −4,1−5i,5−2i ln(3)/5−3 ln(2)/10 +π/10 √
2−1 √
3/2 C 2x−2x2+ 4x3 1,1 +i,−5 + 3i 3 ln(2)/20−ln(3)/10 + 3π/40 π/4−ln(2)/2 1/2 D 3x−9x2/2 + 9x3/2 3,2,−2−i −ln(3)/5 + 3 ln(2)/10 + 3π/20 1/2 1/2
E 2x−2x2 3,−4−i,−4−4i ln(2)/4 + 3π/8 π/4−1/2 −
√3/2
F x+ 3x2/2−5x3/3 1,−4,2−4i 3 ln(2)/20−ln(3)/10 + 3π/40 4/π−1 √ 3/2 G 1 + 3x+ 9x2/2 −1,4−3i,−1 + 4i ln(3)/5−ln(2)/10 +π/40 π/4 −
√3/2
H 1 + 2x+ 2x2+ 8x3/3 3,4 + 4i,−4−5i ln(2)/5−ln(5)/10 + 2 arctan(2)/5 0 1/2 I 1 + 2x+ 2x2−4x3/3 3,1−2i,5−4i ln(5)/20−ln(3)/10 + 3 arctan(2)/10 1/π −
√3/3
J −3x+x2+ 27x3/2 −3,−1−2i,−2−2i ln(5)/10−ln(2)/5 + 3 arctan(2)/5 1/2 √ 3 K 2x+x2−4x3/3 −2,5−1,−2 +i ln(3)/2−ln(5)/4 + 3 arctan(2)/2 −2/3π √
3 L 2x−2x2 1,−5−2i(double) ln(5)/20−ln(3)/10 + 3 arctan(2)/10 4/3π √
3
