’žA n a l i z a M a t e m a t y c z n a - I R o k I n f o r m a t y k i
L i s t a 1 2
O b l i c z y n a s t p u j c e c a Bk i :
( 1 ) a r c s i n x d x ( 2 ) a r c c o s x d x
( 3 ) ( a r c s i n x ) 2 d x ( 4 ) ( a r c c o s x ) 2 d x
x 2 a r c s i n x
" "
( 5 ) · a r c s i n x d x ( 6 ) d x
1 - x 2
( 1 - x 2 ) 3
x 2 d x
"
( 7 ) · a r c t g x d x ( 8 )
1 + x 2
( 1 + 9 x 2 ) a r c t g ( 3 x )
( a r c t g x ) 2
d x
"
( 9 ) d x ( 1 0 )
x 2 + 1
1 - x 2 ( a r c c o s x ) 2
d x x a r c t g x d x
"
( 1 1 ) ( 1 2 )
( 1 + x 2 ) 2
1 - x 2 a r c s i n x
x a r c s i n x d x
( 1 3 ) ( 1 4 ) x a r c s i n x d x
3
2
( 1 - x 2 )
x a r c t g x d x
( 1 5 ) ( 1 6 ) x 2 a r c t g x d x
( x 2 - 1 ) 2
e x + 1
( 1 7 ) x 3 a r c t g x d x ( 1 8 ) d x
e x - 1
2
"
l n x
( 1 9 ) d x ( 2 0 ) e 3 x + e x d x
x
e x - e - x d x
( 2 1 ) d x ( 2 2 )
e x + e - x e 2 x - 1
"
d x
"
( 2 3 ) e x + 1 d x ( 2 4 )
3 + 2 e x
"
e x d x
( 2 5 ) e x 1 + e x d x ( 2 6 )
( e x - 1 ) 2
e x d x e x d x
"
( 2 7 ) ( 2 8 )
e x + 5
3 - 5 e 2 x
d x
( 2 9 ) ( 3 0 ) l n ( x 2 + 1 ) d x
x l n x
"
( 3 1 ) ( l n | x | ) 2 d x ( 3 2 ) l n x + x 2 + 1 d x
l n | x | d x
d x
( 3 3 ) ( 3 4 )
x ( 1 + l n 2 | x | ) x 2
( 3 5 ) ( 4 + 3 x ) 2 l n | x | d x ( 3 6 ) x 3 l n ( x 2 + 3 ) d x
P a t r z t e |:
W . K r y s i c k i , L . W Bo d a r s k i : A n a l i z a M a t e m a t y c z n a w Z a d a n i a c h . C z [ I , s t r . 3 6 4 - 3 7 0
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