CAŁKI - zadania - rozwiązania

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//-->Autorzy:Szemek, mariuszmAnaliza matematyczna w zadaniach, t. 1,W. Krysicki, L. Włodarski - rozwiązaniaCałki nieoznaczone. Całkowanie przez podstawienie i całkowanie przez części.15.2215.2315.2415.2515.2615.2715.2815.2915.3015.3115.3215.3315.3415.3515.3615.3715.3815.3915.4015.4115.4215.4315.4415.455x2−6x + 3−52+2dxx x15.4615.4715.4815.4915.5015.5115.5215.5315.5415.5515.5615.5715.5815.5915.6015.6115.6215.6315.6415.6515.6615.6715.6815.69sin5xcosx dxcosxdx1 + sinxsinxdx, b= 0a+bcosxcosx·esinxdx√x3dxcos2x4tanxdxcos2xx2dxcos2(x3+ 1)(lnx)2dxxdxex+e−xexdx2ex+ 1xln(1 +x2)dx2 + ln|x|dxx61−xdxdxx1−ln2|x|ln|arctanx|dx1 +x22xex(x2+ 1)dxx2dx√1−x6dx(1 +x2) arctanx(π−arcsinx)dx√1−x2xdxx4+ 1x4(1 +x)3dxx2exdxx3exdxx4e2xdx(x2−1)3dxx(x2−x+ 1)(x2+x+ 1)dx(x2+ 4)5xdxxdx1 +x2xdx(x2+ 3)6x2dx, a= 0,x=−aa3+x3√√x3x+4xdx2√x√x x−x4x√dx3x√(3 + 24x)3dx√√√34x−2x2+ 4 5x3√dx63x√33 + 5x2√dxx3√3x + 1dx√a+bxdx√3xdx2x2−1x1 +x2dxx√dx3−5x2x−1√dx3x+1x√dxx2−6x2√dx5x3+ 11exdxx22xe−xdxdx2 cos23xxsin(2x2+ 1)dx1matematyka.plAutorzy:Szemek, mariuszm15.7015.7115.7215.7315.7415.7515.76xcosxdxx2cosxdxx2sin 5xdxexcosxdxe−2xsin 3xdx2excos(3x)dx√xlnxdx15.7715.7815.7915.8015.8115.8215.83(ln|x|)3dx(ln|x|)2dxx5√x(ln|x|)3dxln|x|dxx4(lnx)2√dxxx3(lnx)2dxxnlnx dx, n=−1Całki funkcji wymiernych.16.2616.2716.2816.2916.3016.3116.3216.3316.3416.3516.3616.3716.3816.3916.4016.4116.4216.4316.44(2x + 1)3dxdx(3x−2)43x−4dxx2−x−62x−3dxx2−3x + 3x+ 13dxx2−4x−52x + 6dx2x2+ 3x + 16x−13dxx2−7x+3224x−5dx2x2−5x + 35x + 11dxx2+ 3x−1056x−16dxx2+ 3x−18dxx2+ 2x−1dx6x2−13x + 65+xdx10x +x27xdx4 + 5x2dx−5+ 6x−x2dx1 +x−x2dx2x−3x23x + 2dxx2−x−22x−1dxx2−6x + 916.4516.4616.4716.4816.4916.5016.5116.5216.5316.5416.5516.5616.5716.5816.5916.6016.6116.6216.63x−1dx4x2−4x + 12x−13dx(x−5)23x + 1dx(x + 2)2dx2x2−2x + 5dx3x2+ 2x + 1dx13−6x +x23dx9x2−6x + 2x+1dxx2−x+ 14x−1dx2x2−2x + 12x−1dxx2−2x + 52x−10dxx2−2x + 102x−20dxx2−8x + 253x + 4dxx2+ 4x + 8x+6dxx2−3x+6dxx2+ 36xdxx2+ 4x + 1310x−44dxx2−4x + 204x−5dxx2−6x + 105xdx2 + 3x2matematyka.plAutorzy:Szemek, mariuszm16.6416.6516.6616.6716.6816.6916.7016.7116.7216.7316.7416.7516.7616.7716.7816.7916.80x2dx5x2+ 122x2+ 7x + 20dxx2+ 6x + 257x2+ 7x−176dxx3−9x2+ 6x + 56x3−4x2+ 1dx(x−2)43x2−5x + 2dxx3−2x2+ 3x−62x + 1dx(x2+ 1)2x3+ 2x−6dxx2−x−22x3−19x2+ 58x−42dxx2−8x + 16x4dxx2+ 172x6dx3x2+ 22x4−10x3+ 21x2−20x + 5dxx2−3x + 2x2+ 5x + 41dx(x + 3)(x−1)(x−1)22−x−2617xdx(x2−1)(x2−4)2xdx(x2+ 1)(x2+ 3)10x3+ 110x + 400dx(x2−4x + 29)(x2−2x + 5)4x3−2x2+ 6x−13dxx4+ 3x2−410x3+ 40x2+ 40x + 6dxx4+ 6x3+ 11x2+ 6x16.8116.8216.8316.8416.8516.8616.8716.8816.8916.9016.9116.9216.9316.9416.9516.9616.9716.986x3+ 4x + 1dxx4+x2dxx3−a2xdxx3+x2+xdxx4+x2+ 15x3+ 3x2+ 12x−12dxx4−1615x2+ 66x + 21dx(x−1)(x2+ 4x + 29)4x3+ 9x2+ 4x + 1dxx4+ 3x3+ 3x2+xdxx3(x−1)2(x + 1)dx(x2+x+ 1)23x2−17x + 21dx(x−2)3dx(x2+ 4x + 8)3x3−2x2+ 7x + 4dx(x−1)2(x + 1)2dxx4+ 645x3−11x2+ 5x + 4dx(x−1)4dxx4+ 6x2+ 259x4−3x3−23x2+ 30x−1dx(x−1)4(x + 3)x3−2x2+ 5x−8dxx4+ 8x2+ 163x2+x−2dx(x−1)3(x2+ 1)Całki funkcji niewymiernych. Całki funkcji zawierających pierwiastki z wy-rażenia liniowego.17.617.717.817.917.1017.11√2x + 1dx17.1217.1317.1417.1517.1617.17√x2 + 3xdx√x1−5xdx√x3x−4dxxdx2x + 3x2dx√33x+2x2+ 1√dx3x + 1√4√dx3 + 4xdx√33x−4dx5(2x + 1)3√x3x−4dx√x33x−1dx3matematyka.plAutorzy:Szemek, mariuszm17.1817.1917.2017.2117.2217.2317.2417.2517.26√x42x + 3dxdx√x x+adx√x x−a√xdxx−1√x+1dxx√1+x√dx1−xdx√(x + 1) 1−x√1 +xdx√3xdx√6x+x517.2717.2817.2917.3017.3117.3217.3317.3417.35√3x+ 2x2dx√√x−5+x−7dx√x x+9√x237−2xdx√√dx√x+1+3x+1x−1dx·x−2 (x−1)2dx1−x dx·1+x xxdx√√3x+1−x+1√√3x2−x+ 1√dx3x−1Całki funkcji zawierających pierwiastek kwadratowy z trójmianu kwadrato-wego17.5117.5217.5317.5417.5517.5617.5717.5817.5917.6017.6117.6217.6317.64(8x + 3)dx4x2+ 3x + 1(10x + 15)dx√36x2+ 108x + 77dx√2x−x2dx√7−6x−x2dx√1−9x2dx(2r−x)x(x + 3)dx√1−4x2xdx√1−2x−3x2√1−4x2dx6x + 5√dx6 +x−x2x−5√dx5 + 4x−x2x+1√dx8 + 2x−x26x−x2dx√2x−3dx3−2x−x217.7417.7517.7617.7717.7817.7917.6517.6617.6717.6817.6917.7017.7117.7217.73dxx2+ 3x + 2dx√4x2+ 3x−1dx√x2−x+mdx(x−a)(x−3a)(x + 3)dx√x2+ 2x(3x + 2)dx√x2−5x + 19x+a√dxx2−ax3x−2√dx4x2−4x + 53x + 2√dxx2−4x + 53x−4√dx4x2+ 5x−85x + 2√dx2x2+ 8x−12x +x2dx√√5x−4dx3x2−2x + 13−2x−x2dxx2−4dx4matematyka.plAutorzy:Szemek, mariuszm17.8017.8117.8217.8317.8417.8517.8617.8717.8817.8917.9017.9117.9217.9317.9417.9517.9617.9717.9817.9917.10017.1013x2+ 10x + 9dxx2−3x + 2dx1−x2x2dx√x2+ 2x + 2xdx1−x2ax2+ 1√dxax2+ 2x + 12x2+ 3x + 1√dxx2+ 12x2−ax+a2√dxx2+a2x3−x+ 1√dxx2+ 2x + 2x3+ 2x2+x−1√dxx2+ 2x−1x3dx√x2−4x + 33x3+ 2√dxx2+x+ 1x24x−x2dxx6 +x−x2dxx4dx√5x2+ 4x3+ 5x2−3x + 4√dx2+x+1x2−2x + 105x√dx3x2−5x + 8x3+ 4x2−6x + 3√dx5 + 6x−x2x8 +x−x2dx(2x−5) 2 + 3x−x2dxx3dx√2x2+ 3x5dx√2x2+ 3√x2dx17.10217.10317.10417.10517.10617.10717.10817.10917.11017.11117.11217.11317.11417.11517.11617.11717.11817.11917.12017.12117.12217.123x4dx√3 + 2x +x2dx√x10x−x2dx√(x + 1)x2−1dx√(x + 2) 4−x2dx√x x2+x−1dx√x x2−2x−1dx√(2x−1)x2−1dx√(x + 1) 1 + 2x−3x2dx√(3−2x)x2−4x + 3dx√x x2+x+ 1dx√x x2−1dx√(a−x) a2−x2dx√(x−2)x2−6x + 1dx√x24−x2dx√(x−1)210x−x2dx√x3x2+ 1dx√x32x2+ 2x + 1dx√(x−1)33−2x2dx√x21−4x +x2dx√x31 +x2dx√x43−2x +x2dx√(x−2)41−4x +x2Całki funkcji trygonometrycznych.18.3018.31cos 5x cos 7xdxsin 3x cos 2xdx18.3218.33cos 2x cos 3xdxsinxcos 3xdx5matematyka.pl [ Pobierz całość w formacie PDF ]