03.2 - Całka nieoznaczona.pdf - Zadania - Matematyka podstawowa - aneciakurczaczek

WydziałWILi,BudownictwoiTransport,sem.1

drJolantaDymkowska

Całkanieoznaczona-ci¡gdalszy

(1+3x) 4 1.2 R 3

x 2 −6x+10 dx 1.6 R 4x+5

x 2 −2x+50

2x 2 +2x+1 dx 1.8 R dx

8x 2 −x dx 1.9 R 2dx

x 2 −6x+13 dx

x 2 −9 dx 1.11 R dx

1.12 R 2x+21

1.13 R dx

x 2 (x 2 +4)

(x−2)(x 2 +2x+5) dx 1.15 R x 2

2x 2 +9x−5 dx

x(x−1) 2 1.17 R x 2 −3

x(x+1) 2 dx 1.18 R x

(x+3)(x 2 −2x+10) dx

x 3 +4x dx 1.20 R dx

(x+1) 2 x 3 1.21 R 2x

(x 2 −4) 2 dx

1.22 R dx

x 4 −8x 2 +16

1.23 R dx

x 3 +2x 2 +x+2

1.24 R dx

9x 3 −6x 2 +4x

(x+1) 3 dx 1.26 R x 5 +2

x 4 −1 dx 1.27 R 3x 3

(x−3) 2 dx 1.29 R x 2

(x+2) 2 (x+4) 2 dx 1.30 R x 3 −2x−1

x 2 +x−2 dx

1.31 R x 3 +x 2 +1

x 3 +x 2 dx 1.32 R 2x 5 +6x 3 +1

x 4 +x 2 dx 1.33 R x 3 −3x 2 +5x−9

x 2 −1 dx

x 2 −3x dx

1.34 R 1 x 2

q x

x+1 dx 1.35 R dx

p x−1+ 4 p x−1 1.36 R d x

p x+ 3 p x+ 4 p x

x+2 dx 1.38 R ( p x+1) 2

x dx 1.39 R x+ p 2x−3

1.40 R x 2 + p 1+x

3 p 1+x dx 1.41 R 4 p x+2

x( 3 p x+4 6 p x) dx 1.42 R 3 p 2−3 x

x−1 dx

3 p 3x+4+ 4 p 3x+4 dx 1.44 R q 9x+1

p 2−3x−8 dx

2−x dx

1.45 R dx

1.46 R dx

1.47 R dx

p x 2 +6x+5 dx 1.49 R −6x−5

p −x 2 −3x−2 dx 1.50 R 4x−1

p 9x 2 +6x+5 dx 1.52 Rp

x 2 −6x+5dx 1.53 Rp

p x 2 −10x+9

16x 2 +40x+50dx

1.54 R sin 3 xdx 1.55 R cos 7 xdx 1.56 R sin 4 xcos 5 xdx

1.57 R sin 2 xcos 7 xdx 1.58 R sin 3 xcos 2 xdx 1.59 R cos 3 x

cos 3 x dx 1.62 R 3+sinx

sin 5 x dx

sinx+7cosx dx 1.64 R sinx

3sinx+2cosx−2 dx 1.65 R 1−cosx

1+cosx dx

sin 2 x+sinx dx 1.67 R 1

4+sin 2 x dx 1.68 R 1

4+5sinx dx

sin 2 x+4cos 2 x dx 1.70 R 1

sin 4 x+4cos 2 x dx 1.71 R cos 2 x

5−4sinx+3cosx dx

1.72 R cos 3 x

3sin 2 xcos 2 x−4sin 2 x dx

2sin 3 x−sin 2 x+sinx dx

Zad.1Oblicz:

1.1 R dx

1.4 R dx

x 2 −6x+13

1.5 R −x

(4x−15) 5 dx 1.3 R dx

1.7 R 3x+4

1.10 R 5x+3

x 2 +2x dx

2x 2 −7x+3

1.14 R x

1.16 R dx

1.19 R x 3 −4

x 4 +6x 2 +25 dx

1.25 R 2x 5 −x

1.28 R x+1

1.37 R p x

1.43 R x

p x 2 +2x+2

p 9x 2 −36

p 16x 2 +40x+50

1.48 R 4x−3

1.51 R 36x+1

1.60 R 1

cos 3 x dx 1.61 R sinx

1.63 R 1

1.66 R 1

1.69 R 1

p 9−25x 2 2.5 R xdx

16−9x 4 2.6 R sin(2−3x)dx

4x 3 −7x 2 dx 2.3 R dx

9x 2 +4

2.7 R dx

x(ln 2 x+4)

2.8 R cos(lnx)

x dx 2.9 R e x

p 25−e 2x dx

2.10 R ln x 2 −1 dx 2.11 R ln 2 (4x−3)dx 2.12 R xcos(2x−1)dx

2.13 R x 2

p e x dx 2.14 R 1

sinxdx 2.17 R sin 3 x

3 p cos 2 x dx 2.18 R p sin 2 x+sinxcosxdx

x(x+1) dx

p sin 2 x+2sinx+2 dx 2.20 R sin 2 xcos 2 xdx 2.21 R x 2 sin 2 xdx

2.22 R arcsinx

x 2 dx 2.23 R xarcctgxdx 2.24 R arccos(x+1)dx

2.25 R arctg p x

p x dx 2.26 R x 4 lnxdx 2.27 R dx

x( ln 2 x+1 )lnx

2.28 R ln(x 2 +1)dx 2.29 R arcsin

x+1dx 2.30 R p

9−e x dx

1+e x 2.32 R ln(x 2 −x+1)

x 2 dx 2.33 R lnsinx

e x dx 2.35 R 2x 2 +1

x 2 +1 arctgxdx 2.36 R arccos

sin 2 x dx

q x+1

x+2 dx

p 1+e x dx 2.38 R cos 2 p xdx 2.39 R p tgx

sinxcosxln 2 (tgx) 2.41 R 1 x

q 1− 3 p x

1+ 3 p x dx 2.42 R xarctgx

sin2x dx

(x 2 +1) 2 dx

p x( p x−6)

2.4 R dx

Zad.2Oblicz:

2.1 R dx

2.2 R 3 p

x p 1+lnx dx 2.15 R ln(x+1)−lnx

2.16 R cos 3 x

2.19 R sin2x

2.31 R dx

2.34 R arccose x

2.37 R xe x

2.40 R dx

03.2 - Całka nieoznaczona.pdf

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