10. Całki nieoznaczone
Zadanie 1. Obliczyć całki:
4
tg x � cos5 x dx, arc tg x dx, x � arc sin x dx, ln x dx,
" "
2
cos 2x 1+x2- x2-1
"
"3x +2x+1
dx, x2sin 2x dx, dx, dx,
3
ex
x4-1
x3+x2+x+7
"
"
2
sin
x
3-ctg x
earc" x+x+1
"
dx, x 5 - x dx, dx, dx,
2 4
cos x
1-x2
1+ x3
2x-1+5x+1 4 6
dx, 4 x3 log2 x dx, cos x � sin 3x dx, cos x � sin x dx,
10x
"
"
5
3
2x+4 2 2 1-2x+x2
dx, ctg x dx, cth x dx, 1 - 3x dx, dx
1-x
x2+4x+13
1 2x+5 3x+6 5x+3 dx
"
dx, dx, dx, dx, ,
1+cos x
x2+4x+13 x2+4x+13 x2+4x+13
4x-x2
-22-16x+x2+x3 28+19x+5x2
"3x+5
dx, dx, dx,
-4-4x+3x2+4x3+x4 26+25x+8x2+x3
4x-x2
-14-6x+2x2+7x3+3x4 -10+3x+30x2+13x3+3x4 67-21x+12x2
dx, dx, dx,
-1-x+x2+x3 -8+4x+3x2+x3 13+7x-5x2+x3
"
"
x dx sin x+cos x
"
"x+1
x2 x2 + 4 dx, dx, dx, dx, dx,
3 2
ex+e-x
cos x
x+1 sin x-cos x
dx" 1+x dx dx
"
, dx, , ,
2 2
1-x sin x+2cos x+3
x+1- x-1 3sin -8�sin x�cos +5cos x
6x3-20x2+75x-78 7x3-20x2+71x-66 5x2+30x+65
dx, dx, dx,
x4-6x3+29x2-44x+20 x4-2x2-96x+225 x3+11x2+49x+75
10x2+21x+53
"dx
dx, 6 � x2 � arc tg x dx, 6 � arc sin x dx, ,
x3+4x2+21x+34
x 1+x2
8x+3 x2 dx dx
" " "
dx, , .
1+3x+4x2 3+2x+x2 (x-1) 1-x2