2798

260

1

cosax

∫cosaxdx =

1

sin ax

a

∫sin2 axdx =

x

−

sin 2ax

4a

2

∫ x sin axdx =

1

(sin ax − ax cos ax)

2

a

1

(2 ax sin ax + 2 cos ax − a2 x2 cos ax)

3

a

∫cos2 axdx =

x

+

sin 2ax

4a

2

∫ x cos x axdx =

1

(cos ax + ax sin ax)

2

a

1

3

a

∫sin ax sin bxdx =

sin(a − b)x

−

sin(a + b)x

∫sin ax cos bxdx = −

−

, a2

2(a + b)

∫cos ax cos bxdx =

sin(a − b)x

+

sin(a + b)x

2(a − b)

2(a + b)

∫eaxdx =

1

eax

a

∫ x eaxdx =

e

ax

(ax −1)

2

a

∫ x2 eaxdx =

e

ax

(a2 x2 − 2 ax + 2)

a

3

∫eax sin bxdx =

eax

(a sin bx − b cos bx)

a

2

+ b

2

∫eax cos bxdx =

eax

a

2

+ b

2

dx

1

∫

=

a

arctg x

ab