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INTEGRALITabli ni integrali:
Parcijalna integracija:∫ ∫ ⋅−⋅=⋅ duvvudvu u,v su proizvoljne funkcije
I tip:
=⇒
xxexx
xxxe
xxxx
sinddvu
cos
sin
cos=
II tip:
=⇒
xxxx
x
xxxx
xx
arcsinddvlnu
arccos
arcsinlnarccos
=
III tip: integrali u parovima npr.:
xxe
xxex
x
dsinI
dcosI
2
1
∫∫
=
=
...II...II
sindcos=dvu
21
21
=+−=+
⇒
=
xxxe x
∫
∫
∫∫
∫
∫
∫
∫
∫
∫
∫
∫
∫
∫∫
∫
∫
∫
∫
∫∫
+−=
+=
+=
+=
++−
=−
+±=±
+±=±
+±+=±
+−+
=−
+=+
+=−
+−=
+=
+−=
+=
+=
+=
+=
++
=
+=
=⋅
+
Cxdxx
Cxdxx
Cxx
Cxxdx
Caxax
aaxdx
Caxax
xdx
Caxax
xdx
Caxxax
dx
Cxx
xdx
Cxx
dx
Cxx
dx
Cxx
dx
Cxx
dx
Cxxdx
Cxxdx
Ca
adxa
Cedxe
Cxx
dx
Cxa
dxx
Cxdx
Cdx
xx
xx
aa
cothsinh
1
tanhcosh
1
sinhcosh
coshsinh
ln21
ln21
ln
11ln
21
1
arctan1
arcsin1
cotsin
tancos
cossin
sincosln
ln
)1(1
0
2
2
22
2222
22
22
22
22
2
2
2
2
2
1