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Alapintegrálok - Alap integrálok táblázat
Course: Matematika A1
85 Documents
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University: Budapesti Muszaki és Gazdaságtudományi Egyetem
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Alapintegr´alok
I
(Df´es DF)
f(x)
(faz adott f¨uggv´eny)
F(x)
(Faz fegy primit´ıv f¨uggv´enye)
Rxn
(n= 0,1,2, . . .)
xn+1
n+ 1
(0,+∞)1
xln x
(−∞,0) 1
xln(−x)
(−∞,0) vagy (0,+∞)
1
xn
(n= 2,3,4, . . .)
1
1−n·1
xn−1
(0,+∞)xα
(α∈R, α 6=−1)
xα+1
α+ 1
Rexex
(0,+∞)ax
(a∈(0,+∞), a 6= 1)
ax
ln a
Rsin x−cos x
Rcos xsin x
(−
π
2,π
2)tg x−ln cos x
(0, π)ctg xln sin x
(−
π
2,π
2)1
cos2xtg x
(0, π)1
sin2x−ctg x
I
(Df´es DF)
f(x)
(faz adott f¨uggv´eny)
F(x)
(Faz fegy primit´ıv f¨uggv´enye)
Rsh xch x
Rch xsh x
Rth xln ch x
(0,+∞)cth xln sh x
(−∞,0) cth xln sh (−x)
R1
ch2xth x
(−∞,0) vagy (0,+∞)1
sh2x−cth x
R1
1 + x2
arctg x
=π
2−arcctg x
(−1,1) 1
1−x2arth x=1
2·ln 1 + x
1−x
(−∞,−1) vagy (1,+∞)1
1−x2arcth x=1
2·ln x+ 1
x−1
R1
√1 + x2arsh x= ln(x+√1 + x2)
(−1,1) 1
√1−x2
arcsin x
=π
2−arccos x
(1,+∞)1
√x2−1arch x= ln(x+√x2−1)
(−∞,−1) −1
√x2−1arch (−x) = ln(−x+√x2−1)
