Formulario De Calculo Integral Integrales.docx
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INTEGRALES BΓSICAS β« π₯ π ππ₯ =
π₯ π+1 +π π+1
β« ππ₯ π ππ₯ = π (
π₯ π+1 )+π π+1
β«(πΒ΄(π₯) Β± πΒ΄(π₯))ππ₯ = β« πΒ΄(π₯)ππ₯ Β± β« πΒ΄(π₯)ππ₯
β«
π+π+π π
π
π
π
ππ₯ = β« π ππ₯ + β« π ππ₯ + β« π ππ₯
1 β« ππ₯ = ln|π₯| + π π₯ β« β«
ππ’ = ln|π’| + π π’ ππ’ βπ’
= 2βπ’ + π
β« π ππ₯+π ππ₯ =
1 ππ₯+π π +π π
INTEGRALES ESPECIALES β« β« β«
π₯2
ππ₯ 1 π₯βπ = ln | |+π 2 βπ 2π π₯ + π
π₯2
ππ₯ 1 π₯ = ππππ‘ππ + π 2 +π π π
π2
ππ₯ 1 π+π₯ = ln | |+π 2 βπ₯ 2π π β π₯
INTEGRALES ESPECIALES β«
β«
β«
ππ₯ βπ₯ 2
β π2
ππ₯ βπ₯ 2
+ π2
ππ₯ βπ2
β
π₯2
= ln |π₯ + βπ₯ 2 β π2 | + π = ln |π₯ + βπ₯ 2 + π2 | + π π₯ = πππ₯π ππ + π π
π₯ π+1 +π π+1
β« ππ₯ π ππ₯ = π (
π₯ π+1 )+π π+1
β«(πΒ΄(π₯) Β± πΒ΄(π₯))ππ₯ = β« πΒ΄(π₯)ππ₯ Β± β« πΒ΄(π₯)ππ₯
β«
π+π+π π
π
π
π
ππ₯ = β« π ππ₯ + β« π ππ₯ + β« π ππ₯
1 β« ππ₯ = ln|π₯| + π π₯ β« β«
ππ’ = ln|π’| + π π’ ππ’ βπ’
= 2βπ’ + π
β« π ππ₯+π ππ₯ =
1 ππ₯+π π +π π
INTEGRALES ESPECIALES β« β« β«
π₯2
ππ₯ 1 π₯βπ = ln | |+π 2 βπ 2π π₯ + π
π₯2
ππ₯ 1 π₯ = ππππ‘ππ + π 2 +π π π
π2
ππ₯ 1 π+π₯ = ln | |+π 2 βπ₯ 2π π β π₯
INTEGRALES ESPECIALES β«
β«
β«
ππ₯ βπ₯ 2
β π2
ππ₯ βπ₯ 2
+ π2
ππ₯ βπ2
β
π₯2
= ln |π₯ + βπ₯ 2 β π2 | + π = ln |π₯ + βπ₯ 2 + π2 | + π π₯ = πππ₯π ππ + π π
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