integration of ((8(x+a))/(x^2+a^2))dx. using trig. sub.

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Expert Solution

Soln 8(6+a) 22 ta? dal: let a tano. Then, da za see? odo. SO) a²ta? 8 J 8(reta) dre 8 (a tang ta) asec? odo a² tan²ota? ar tan 0+1) seczo do a? (tan20+!) (tano +1) seczo do sec? o [: sec²o- tano = 8Stan +1) de =] 8 B[ln | sec ol + o] + C, where.c c'is the constant of integration. D- a tano ,.-> tan o= 2 a So, seco= + It tanzo =t It 21 92 17 Ja² +212 Jaceta2 Isecol and na Therefore, ätano a tano = 2 => 0= => 0 = thn 12 dre 8) inx²+62 +tant of inpatien) x?ta2 8 in ( 22 +22] sin la') + tanteria +ch 8 + tant en )+c -

= 8 in (22+62)²_8In(a) + tenlle a te' = 8x In (22 +22) - 8|1(a) + tarile not c' 4 11(x2+a2) + tant pour) + C , where e= c'-elrica) a

milcah answered 1 year ago

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