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1.



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((Q 1 ))

f(x) (a, b) F(x), ...

((V ))

(x) = F(x)

((V ))

(x) = (x)

((V +))

(x) = f(x)

((V ))

f(x) = F(x)

((Q 1))

F(x) f(x) = cos x ...

((V ))

- cos x + C

((V ))

- sin x + C

((V +))

sin x + C

((V ))

cos x + C

((Q 1 ))

...

((V ))

arctg x + C

((V ))

arcctg x + C

((V ))

ctg x + C

((V +))

tg x + C

((Q 1))

F(x) - f(x). F(x) f(x) :

((V ))

F(x) = F(x) + f(x)

((V ))

F(x) = f(x)

((V +))

F(x) = F(x) + C

((V ))

F(x) = F(x)

((Q 1))

F(x) f(x) = x :

((V ))

x + C

((V ))

- x + C

((V +))

((V ))

((Q 1))

F(x) f(x):

((V 1 1))

((V 1 2))

((V 1 3))

((V 1 4))

((V 1 5))

((V 1 6))

((V 2 1 ))

((V 2 2 ))

((V 2 3 ))

((V 2 4 ))

((V 2 5 ))

((V 2 6 ))

((Q 1 ))

F(x) - f(x). ...

((V ))

F(x)

((V ))

F(x) + f(x)

((V+))

F(x) + C

((V))

f(x) + C, -

((Q 1 ))

- ...

((V))

f(x)

((V))

F(x)

((V+))

f(x)dx

((V))

F(x)dx

F(x) - f(x)

((Q 1 ))

F(x) - f(x). ...

((V))

f(x)

((V))

F(x)

((V+))

f(x) + C

((V))

F(x) + C

-

((Q 1 ))

...

((V))

((V +))

((V))

((V))

((Q 1 ))

...

((V))

((V +))

+

((V))

2

((V))

2 +

((Q 1))

:

((V 1 1 ))

((V 1 2 ))

((V 1 3 ))

((V 1 4 ))

((V 1 5 ))

((V 1 6 ))

((V 2 1 ))

((V 2 2 ))

((V 2 3 ))

((V 2 4 ))



((V 2 5 ))

((V 2 6 ))

((Q 1))

:

((V 1 1 ))

((V 1 2 ))

((V 1 3 ))

((V 1 4 ))

((V 1 5 ))

((V 1 6 ))

((V 2 1 ))

((V 2 2 ))

((V 2 3 ))

((V 2 4 ))

((V 2 5 ))

((V 2 6 ))

((Q 1))

:

((V 1 1 ))

((V 1 2 ))

((V 1 3 ))

((V 1 4 ))

:

((V 1 5 ))

((V 1 6 ))

((V 2 1 ))

((V 2 2 ))

((V 2 3 ))

((V 2 4 ))

((V 2 5 ))

((V 2 6 ))

((Q 1))

...

((V))

x + C

((V ))

2x2 + C

((V +))

((V ))

2x + C

((Q 1 ))

...

((V ))

((V ))

((V +))

((V ))

((Q 1 ))

...

((V ))

((V +))

((V ))

((V ))

((Q 1 ))

...

((V))

x = t

((V ))

((V +))

t = x2

((V ))

((Q 1))

...

((V ))

e2x + C

((V ))

((V +))

((V ))

2e2x + C

((Q 1 ))

...

((V +))

t = lnx

((V ))

((V ))

t = ln3x

((V ))

t = x

((Q 1 ))

...

((V +))

((V ))

((V ))

((V ))

((Q 1 ))

...

((V ))

((V ))

(x2 + 4) + C

((V ))

ln(x2 + 4) + C

((V +))

((Q 1))

:

((V 1 1 ))

((V 1 2 ))

((V 1 3 ))

((V 1 4 ))

((V 1 5 ))

((V 1 6 ))

((V 2 1 ))

((V 2 2 ))

((V 2 3 ))

((V 2 4 ))

((V 2 5 ))

((V 2 6 ))

((Q 1 ))

. òudv ...

((V +))

uv - òvdu

((V ))

u - òvdu

((V ))

vu - òvdu

((V ))

v - òudv

((Q 1 ))

òx2lnxdx u = ...

((V ))

x2

((V ))

x

((V ))

xlnx

((V +))

lnx

((Q 1 ))

òx2cos 2xdx u = ...

((V ))

cos2x

((V +))

x2

((V ))

xcos2x

((V ))

x

((Q 1 ))

òxe-xdx ...

((V ))

((V +))

((V ))

((V ))

((Q 1 ))

òarctgxdx ...

((V ))

((V +))

((V ))

((V ))

((Q 1 ))

...

((V ))

(x a) + C

((V ))

((V +))

ln| x a | + C

((V ))

((Q 1 ))

...

((V ))

(x + 2)3 + C

((V +))

((V ))

2(x + 2)2 + C

((V ))

((Q 1 ))

...

((V +))

arctg(x + 1) + C

((V ))

((V ))

((V ))

((Q 1 ))

...

((V ))

((V +))

((V ))

((V ))

((Q 1 ))

...

((V ))

ln(x2 + 4) + C

((V ))

((V +))

((V ))

((Q 1 ))

...

((V ))

arctg(x + 2) + C

((V ))

((V +))

((V ))

((Q 1 ))

...

((V ))

ln| x2 - 4x + 8 | + C

((V +))

((V ))

((V ))

((Q 1 ))

...

((V ))

ln| x2 - 4x + 5 | + C

((V ))

ln| x2 - 4x + 5 |

((V +))

ln| x2 - 4x + 5 | + 9arctg (x - 2) + C

((V ))

arctg (x - 2) + C

((Q 1 ))

...

((V ))

ln | x2 + 4 | + C

((V +))

((V ))

((V ))

((Q 1 ))

( ) (Pn(x), Qm(x) - n m) , ...

((V ))

n £ m

((V ))

n > m

((V +))

n < m

((V ))

n = m

((Q 1 ))

...

((V ))

ln | x - 2 | - ln | x + 5 | + C

((V +))

ln |( x - 2)( x + 5)| + C

((V ))

ln | x + 5 | - ln | x - 2 | + C

((V ))

((Q 1 ))

...

((V +))

((V ))

((V ))

((V ))

((Q 1 ))

...

((V ))

sin 2x + C

((V +))

((V ))

((V ))

- sin 2x + C

((Q 1))

...

((V ))

cos 3x + C

((V ))

((V ))

- cos 3x + C

((V +))

((Q 1 ))

...

((V ))

ctg x + C

((V ))

- ctg x + C

((V ))

tg2x + C

((V +))

((Q 1))

...

((V ))

((V ))

((V +))

((V ))

((Q 1))

...

((V ))

((V ))

((V ))

((V +))

((Q 1))

...

((V ))

((V ))

((V +))

((V ))

((Q 1 ))

...

((V ))

((V ))

((V +))

((V ))

((Q 1 ))

...

((V ))

2(x - ln (x + 1)) + C

((V +))

((V ))

2(x - ln (x + 1)) + C

((V ))

((END))





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