Таблица интегралов

R

f(x)dx = F (x) + c; F 0(x) = f(x)

1dx = x + c

n+1

R

xndx = xn+1

R

dx

p

= 2px

x

R

dxx2 = ¡x1

x

R

axdx =

a

ln a

R

exdx = ex

dx

R

x = ln x

R

cos xdx = sin x

R

sin xdx =

¡

cos x

dx

R

= ¡ ctg x

sin2 x

R

dx

= tg x

cos2 x

R

dx

=

ctg x

sin2 x

R

p

dx

=¡arcsin x

1¡x2

R

dx

= arctg x

x2+1

R

dx

1

=

a arctg x=a

x2+a2

R

p

dx

= arcsin x=a

a2¡x2

R

dx

1

x a

=

ln x¡+a

x2¡a2

2a

R

dx

p

= ln(x + px2 + m)

x2+m

R

sindxx = ln tg x2

R

R

n+1

undu = un+1

R

du

= 2pu

p

u

R

duu2 = ¡u1

u

R

audu =

a

ln a

R

eudu = eu

du

R

u = ln u

R

cos udu = sin u

R

sin udu = ¡ cos u

R

du

= tg u

R

R

cos2u

=

du

ctgu

2

u

sin

=¡arcsin u

p

du

1¡u2

R

du

= arctg u

2

R

R

u +1

du

1

=

a arctg u=a

u2+a2

p

du

= arcsin u=a

a2¡u2

R

du

1 u a

=

ln u¡+a

u2¡a2

2a

R

du

p

= ln(u + pu2 + m)

u2+m

R

sinudu = ln tg u2

R