ВУЗ:
Составители:
Рубрика:
Z
adu = au + C,
a ∈ R, C = , u = u(x)
.
Z
u
m
du =
u
m+1
m + 1
+ C,
m 6= −1
.
Z
du
√
u
= 2
√
u + C,
Z
e
u
du = e
u
+ C.
Z
du
u
= ln |u|+ C,
Z
a
u
du =
a
u
ln a
+ C.
Z
cos udu = sin u + C,
Z
sin udu = −cos u + C.
Z
du
cos
2
u
= u + C,
Z
du
sin
2
u
= − u + C.
Z
du
√
a
2
− u
2
= arcsin
u
a
+ C,
Z
du
√
a
2
+ u
2
=
1
a
u
a
+ C.
Z
du
√
u
2
± a
2
= ln
u +
p
u
2
± a
2
+ C.
Z
du
u
2
− a
2
=
1
2a
ln
u − a
u + a
+ C.
cos(α ± β) = cos α cos β ∓ sin α sin β.
sin(α ± β) = sin α cos β ± cos α sin β.
cos
2
α =
1 + cos 2α
2
, sin
2
α =
1 − cos 2α
2
.
x =
1
2
e
x
− e
−x
, x =
1
2
e
x
+ e
−x
, x =
x
x
.
Ïðèëîæåíèå
Òàáëèöà îñíîâíûõ èíòåãðàëîâ
Z
adu = au + C, a ∈ R, C = onst, u = u(x) .
um+1
Z
um du =
+ C, m 6= −1 .
m+1
du √
Z Z
√ = 2 u + C, eu du = eu + C.
u
du au
Z Z
= ln |u| + C, au du = + C.
u ln a
Z Z
cos udu = sin u + C, sin udu = − cos u + C.
du du
Z Z
= tgu + C, = − tgu + C.
cos2 u sin2 u
du u du 1 u
Z Z
√ = arcsin + C, √ = ar tg + C.
a2 − u2 a a2 + u2 a a
du
Z p
√ = ln u + u2 ± a2 + C.
2
u ±a 2
du 1 u−a
Z
2 2
= ln + C.
u −a 2a u+a
Îñíîâíûå òðèãîíîìåòðè÷åñêèå îðìóëû
cos(α ± β) = cos α cos β ∓ sin α sin β.
sin(α ± β) = sin α cos β ± cos α sin β.
1 + cos 2α 1 − cos 2α
cos2 α = , sin2 α = .
2 2
1 x 1 x shx
e − e−x , e + e−x , thx =
shx = hx = .
2 2 hx
52
