Tính các tích phân bất định sau:
a)$ \int\limits_{}^{}\tan^8 x dx$
b) $\int\limits_{}^{} \frac{ dx }{ 3x ^ {2} - 2 } $
c) $ \int\limits_{}^{}\frac{x^4}{ x^ {2} -1}dx$
d) $\int\limits_{}^{}\left (\cot x- \tan x\right )^{2}dx$
 
e)$ \int\limits_{}^{}\frac{1+e^{3x}}{1+e^{x}}dx$
f)$ \int\limits_{}^{}\sqrt{e^{2x}+e^{-2x}+2}dx$ 
chắc là nhất thiết rùi bạn :)) –  nguyentienthanhqn 08-10-12 11:34 PM
Có nhất thiết phải thế không bạn? –  Trần Nhật Tân 08-10-12 11:33 PM
c)
$ \frac{x^{4}}{x^{2}-1}=\frac{\left ( x^{4}-1 \right )+1}{x^{2}-1}=x^{2}+1+\frac{1}{2}\left ( \frac{1}{x-1}-\frac{1}{x+1} \right )$
$\Rightarrow \int\limits \frac{x^4}{x^2-1}dx = \int\limits \left[ {x^2+1+\frac{1}{2}   \left ( \frac{1}{x-1} -\frac{1}{x+1}  \right ) } \right] dx$
                                    $=\frac{x^3}{3}+x+\frac{1}{2} \ln |\frac{x-1}{x+1} | +C $
b)$ \frac{1}{3x^2-2}=\frac{1}{3}.\frac{1}{x^{2}-\frac{2}{3}}=\frac{1}{2\sqrt{6}}\left ( \frac{1}{x-\sqrt{\frac{2}{3}}}-\frac{1}{x+\sqrt{\frac{2}{3}}} \right )$
$\Rightarrow \int\limits \frac{dx}{3x^2-2}=\frac{1}{2 \sqrt{6} } \int\limits \left[ {\frac{1}{x- \sqrt{\frac{2}{3}  } }- \frac{1}{x+ \sqrt{\frac{2}{3} } }} \right]dx$
                               $= \frac{1}{2 \sqrt{6} } \ln |\frac{x- \sqrt{\frac{2}{3} }  }{x+ \sqrt{\frac{2}{3} }  } |+C$
                               $=\frac{1}{2 \sqrt{6} }\ln |\frac{\sqrt{3}x-\sqrt{2}}{\sqrt{3}x+\sqrt{2}}|+C$
a)$ \tan ^{8}x=\left (\tan ^{8}x+\tan ^{6}x \right )-\left ( \tan ^{6}x+\tan ^{4}x \right )+\left ( \tan ^{4}x+\tan ^{2}x \right )-\left ( \tan ^{2}x+1 \right )+1$
$ =\tan ^{6}x\left ( \tan ^{2}x+1 \right )-\tan ^{4}x\left ( \tan ^{2}x+1 \right )+\tan ^{2}x\left ( \tan ^{2}x+1 \right )-\left ( \tan ^{2}x+1 \right )+1$
$=\tan ^{6}x\left ( \tan x \right )^{'}-\tan ^{4}x\left ( \tan x \right )^{'}+\tan ^{2}x\left ( \tan x \right )^{'}-\left ( \tan x \right )^{'}+1$
$\Rightarrow \int\limits \tan ^8xdx=\int\limits   \left ( \tan ^6x-\tan ^4x+\tan ^2x-1 \right ) d(\tan x)+ \int\limits dx$
                                $= \frac{\tan ^7x}{7}- \frac{\tan ^5x}{5}+\frac{\tan ^3x}{3}-\tan x+C   $
e)$e^{2x}+e^{-2x}+2=\left (e^{x}+e^{-x} \right )^{2} $
$\Rightarrow \int\limits \sqrt{e^{2x}+e^{-2x}+2}dx=\int\limits\left ( e^x+e^{-x} \right ) dx= e^x-e^{-x}+C $
a) $ \frac{1+e^{3x}}{1+e^{x}}=1-e^{x}+e^{2x}$
$\Rightarrow \int\limits \frac{1+e^{3x}}{1+e^x}dx $
$ =\int\limits (1-e^x+e^{2x})dx$
$= x-e^x+\frac{1}{2}e^{2x}+C $
d)$\left ( \cot x-\tan x \right )^{2}=\cot ^{2}x+\tan ^{2}x-2=\left ( 1+\cot ^{2}x\right )+\left ( 1+\tan ^{2}x\right )-4 $
$\Rightarrow \int\limits\left (\cot x-\tan x \right )^2dx = \int\limits \left[ {  \left ( 1+ \cot ^2x \right ) +   \left ( 1+\tan ^2x \right )-4 } \right]dx $
                                                      $=- \int\limits d   \left ( \cot x \right )+ \int\limits d (\tan x) - \int\limits 4 dx$
                                                      $=- \cot x+\tan x-4x+C$

Bạn cần đăng nhập để có thể gửi đáp án

Chat chit và chém gió
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:46 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:47 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:48 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:49 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:50 PM
  • hoahoa.nhynhay: . 11/5/2018 1:39:50 PM
  • hoahoa.nhynhay: ..................... 11/5/2018 1:39:52 PM
  • vinhlyle: hi 11/10/2018 8:03:02 PM
  • ๖ۣۜBossღ: 3:00 AM 11/11/2018 10:17:11 PM
  • quanghungnguyen256: sao wweb cứ đăng nhập mãi nhĩ, k trả lời đc bài viết nữa 11/30/2018 4:35:45 PM
  • quanghungnguyen256: web nát r à 11/30/2018 4:36:19 PM
  • quanghungnguyen256: 11/11/2018 h là 30/11. oi web chắt k ai dùng r hả 11/30/2018 4:36:44 PM
  • quanghungnguyen256: rofum ngon thế mà sao admin lại k nâng cấp nhỡ 11/30/2018 4:37:07 PM
  • nguyenlena2611: talk_to_the_hand 12/24/2018 9:24:22 PM
  • nguyenlena2611: big_grinsurpriseblushing 12/24/2018 9:28:35 PM
  • Việt EL: ^^ 2/16/2019 8:37:21 PM
  • Việt EL: he lô he lô 2/16/2019 8:37:34 PM
  • Việt EL: y sờ e ny guan hiar? 2/16/2019 8:38:15 PM
  • Việt EL: èo 2/16/2019 8:38:32 PM
  • Việt EL: éo có ai 2/16/2019 8:40:48 PM
  • dfgsgsd: Hế lô 2/21/2019 9:52:51 PM
  • dfgsgsd: Lờ ôn lôn huyền ..... 2/21/2019 9:53:01 PM
  • dfgsgsd: Cờ ắc cắc nặng.... 2/21/2019 9:53:08 PM
  • dfgsgsd: Chờ im.... 2/21/2019 9:53:12 PM
  • dfgsgsd: Dờ ai dai sắc ...... 2/21/2019 9:53:23 PM
  • dfgsgsd: ờ ưng nưng sắc.... 2/21/2019 9:53:37 PM
  • dfgsgsd: Mờ inh minh huyền.... đờ ep nặng... trờ ai... quờ a sắc.... đờ i.... 2/21/2019 9:54:11 PM
  • nln: winking 2/28/2019 9:02:14 PM
  • nln: big_grin 2/28/2019 9:02:16 PM
  • nln: smug 2/28/2019 9:02:18 PM
  • nln: talk_to_the_hand 2/28/2019 9:02:20 PM
  • nln: Specialise 2/28/2019 9:51:54 PM
  • nlnl: But they have since become two much-love 2/28/2019 10:03:10 PM
  • dhfh: sad 3/2/2019 9:27:26 PM
  • ๖ۣۜNatsu: allo 3/3/2019 11:39:32 PM
  • ffhfdh: reyeye 3/5/2019 8:53:26 PM
  • ffhfdh: ủuutrr 3/5/2019 8:53:29 PM
  • dgdsgds: ujghjj 3/24/2019 9:12:47 PM
  • ryyty: ghfghgfhfhgfghgfhgffggfhhghfgh 4/9/2019 9:34:48 PM
  • gdfgfd: gfjfjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj 4/14/2019 9:53:38 PM
  • gdfgfd: sadsadsadsadsadsad 4/14/2019 9:59:30 PM
  • fdfddgf: trâm anh 4/17/2019 9:40:50 PM
  • gfjggg: a lot of advice is available for college leavers 5/10/2019 9:32:12 PM
  • linhkim2401: big_hug 7/3/2019 9:35:43 AM
  • ddfhfhdff: could you help me do this job 7/23/2019 10:29:49 PM
  • ddfhfhdff: i don't know how to 7/23/2019 10:30:03 PM
  • ddfhfhdff: Why you are in my life, why 7/23/2019 10:30:21 PM
  • ddfhfhdff: Could you help me do this job? I don't know how to get it start 7/23/2019 10:31:45 PM
  • ddfhfhdff: big_grinwhistling 7/23/2019 10:32:50 PM
  • ddfhfhdff: coukd you help me do this job 7/23/2019 10:39:22 PM
  • ddfhfhdff: i don't know how to get it start 7/23/2019 10:39:38 PM
  • huy31012002:9/13/2019 10:43:52 PM
  • huongpha226: hello 11/29/2019 8:22:41 PM
  • hoangthiennhat29: pig 4/2/2020 9:48:11 PM
  • cutein111: . 4/9/2020 9:23:18 PM
  • cutein111: . 4/9/2020 9:23:19 PM
  • cutein111: . 4/9/2020 9:23:20 PM
  • cutein111: . 4/9/2020 9:23:22 PM
  • cutein111: . 4/9/2020 9:23:23 PM
  • cutein111: hello 4/9/2020 9:23:30 PM
  • cutein111: mấy bạn 4/9/2020 9:23:33 PM
  • cutein111: mấy bạn cần người ... k 4/9/2020 9:23:49 PM
  • cutein111: mik sẽ là... của bạn 4/9/2020 9:23:58 PM
  • cutein111: hihi 4/9/2020 9:24:00 PM
  • cutein111: https://www.youtube.com/watch?v=EgBJmlPo8Xw 4/9/2020 9:24:12 PM
  • nhdanfr: Hello 9/17/2020 8:34:26 PM
  • minhthientran594: hi 11/1/2020 10:32:29 AM
  • giocon123fa: hi mọi ngừi :33 1/31/2021 10:31:56 PM
  • giocon123fa: call_me 1/31/2021 10:32:46 PM
  • giocon123fa: không còn ai nữa à? 1/31/2021 10:36:35 PM
  • giocon123fa: toi phải up cái này lên face để mọi người vào chơilaughing) 1/31/2021 10:42:37 PM
  • manhleduc712: hí ae 2/23/2021 8:51:42 AM
  • vaaa: f 3/27/2021 9:40:49 AM
  • vaaa: fuck 3/27/2021 9:40:57 AM
  • L.lawiet: l 6/4/2021 1:26:16 PM
  • tramvin1: . 6/14/2021 8:48:20 PM
  • dothitam04061986: solo ff ko 7/7/2021 2:47:36 PM
  • dothitam04061986: ai muốn xem ngực e ko ạ 7/7/2021 2:49:36 PM
  • dothitam04061986: e nứng 7/7/2021 2:49:52 PM
  • Phương ^.^: ngủ hết rồi ạ? 7/20/2021 10:16:31 PM
  • ducanh170208: hi 8/15/2021 10:23:19 AM
  • ducanh170208: xin chao mọi người 8/15/2021 10:23:39 AM
  • nguyenkieutrinh: hiu lo m.n 9/14/2021 7:30:55 PM
  • nguyenngocha651: Xin chào tất cả các bạn 9/20/2021 3:13:46 PM
  • nguyenngocha651: Có ai onl ko, Ib với mik 9/20/2021 3:14:08 PM
  • nguyenngocha651: Còn ai on ko ạ 9/20/2021 3:21:34 PM
  • nguyenngocha651: ai 12 tủi, sinh k9 Ib Iw mik nhố 9/21/2021 10:22:38 AM
Đăng nhập để chém gió cùng mọi người
  • dvthuat
  • hoàng anh thọ
  • nhungtt0312
  • Xusint
  • tiendat.tran.79
  • babylove_yourfriend_1996
  • thaonguyenxanh1369
  • hoangthao0794
  • zzzz1410
  • watashitipho
  • HọcTạiNhà
  • Cá Hêu
  • peonycherry
  • phanqk1996
  • giothienxung
  • khoaita567
  • nguyentranthuylinhkt
  • maimatmet
  • minh.mai.td
  • quybalamcam
  • m_internet001
  • bangtuyettrangsocola
  • chizjzj
  • vuivequa052
  • haibanh237
  • sweetmilk1412
  • panhhuu
  • mekebinh
  • Nghịch Thuỷ Hàn
  • Lone star
  • LanguaeofLegend
  • huongduong2603
  • i_love_you_12387
  • a ku
  • heohong_congchua
  • impossitable111
  • khanh
  • ๖ۣۜJinღ๖ۣۜKaido
  • huynhhoangphu.10k7
  • namduong2016
  • vycreepers
  • Bảo Phươngg
  • Yurika Yuki
  • tinysweets98
  • Thùy Trang
  • Hàn Thiên Dii
  • ๖ۣۜConan♥doyleღ
  • LeQuynh
  • thithuan27
  • huhunhh
  • ๖ۣۜDemonღ
  • nguyenxinh6295
  • phuc642003
  • diephuynh2009
  • Lê Giang
  • Han Yoon Min
  • ...
  • thuyvan
  • Mặt Trời Bé
  • DoTri69
  • bac1024578
  • Hạ Vân
  • thuong0122
  • nhakhoahoc43
  • tuanngo.apd
  • Đức Vỹ
  • ๖ۣۜCold
  • Lethu031193
  • salihova.eldara