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Question Number 57418 by Abdo msup. last updated on 03/Apr/19

calculate ∫_(−1) ^4 ((∣x−1∣+∣x−2∣)/(∣x^2 −9∣ +x^2 +16))dx

calculate∫−14∣x−1∣+∣x−2∣∣x2−9∣+x2+16dx

Commented by kaivan.ahmadi last updated on 03/Apr/19

∫_(−1) ^1 ((1−x+2−x)/(9−x^2 +x^2 +16))dx+∫_1 ^2 ((x−1+2−x)/(9−x^2 +x^2 +16))dx+ ∫_2 ^3 ((x+1+x+2)/(9−x^2 +x^2 +16))dx+∫_3 ^4 ((x−1+x+2)/(x^2 −9+x^2 +16))dx= ∫_(−1) ^1 ((−2x+3)/(25))dx+∫_1 ^2 (1/(25))dx+ ∫_2 ^3 ((2x+3)/(25))dx+∫_3 ^4 ((2x+1)/(2x^2 +7))dx now you can calculate each of this integral easily

∫−111−x+2−x9−x2+x2+16dx+∫12x−1+2−x9−x2+x2+16dx+∫23x+1+x+29−x2+x2+16dx+∫34x−1+x+2x2−9+x2+16dx=∫−11−2x+325dx+∫12125dx+∫232x+325dx+∫342x+12x2+7dxnowyoucancalculateeachofthisintegraleasily

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