{"common":{"save":0,"post_id":"8058","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5924","post_id":"8058","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho&nbsp;<span class=\"math-tex\">$\\int\\limits_1^3\\dfrac{x+3}{x^2+3x+2}dx=a\\ln2+b\\ln3+c\\ln5$<\/span>&nbsp;v\u1edbi&nbsp;<span class=\"math-tex\">$a,b,c$<\/span>&nbsp;l&agrave; c&aacute;c s\u1ed1 nguy&ecirc;n. Gi&aacute; tr\u1ecb c\u1ee7a&nbsp;<span class=\"math-tex\">$a+b+c$<\/span>&nbsp;b\u1eb1ng:<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> 2","<strong>C.<\/strong> 3","<strong>D.<\/strong> 1"],"correct":"2","level":"2","hint":"<p>S\u1eed d\u1ee5ng t&iacute;nh ch\u1ea5t t&iacute;ch ph&acirc;n&nbsp;<\/p><p><span class=\"math-tex\">$\\int\\limits_a^b\\Big[f(x)\\pm g(x)\\Big]dx=\\int\\limits_a^bf(x)dx\\pm\\int\\limits_a^bg(x)dx$<\/span><\/p><p><span class=\"math-tex\">$\\int\\limits_a^b\\dfrac{1}{ax+b}dx=\\dfrac{1}{a}.\\ln|ax+b|\\bigg|_a^b$<\/span><\/p>","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;2<\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\dfrac{x+3}{x^2+3x+2}=\\dfrac{x+3}{(x+1)(x+2)}=\\dfrac{2}{x+1}-\\dfrac{1}{x+2}$<\/span><\/p><p>Do \u0111&oacute;&nbsp;<span class=\"math-tex\">$\\int\\limits_1^3\\dfrac{x+3}{x^2+3x+2}dx=\\int\\limits_1^3\\dfrac{2}{x+1}dx-\\int\\limits_1^3\\dfrac{1}{x+2}dx$<\/span><\/p><p><span class=\"math-tex\">$=\\Big(2\\ln|x+1|-\\ln|x+2|\\Big)\\bigg|_1^3$<\/span><\/p><p><span class=\"math-tex\">$=2(\\ln4-\\ln2)-(\\ln5-\\ln3)$<\/span><\/p><p><span class=\"math-tex\">$=2\\ln2+\\ln3-\\ln5$<\/span><\/p><p>Suy ra&nbsp;<span class=\"math-tex\">$a=2,b=1,c=-1$<\/span>&nbsp;n&ecirc;n&nbsp;<span class=\"math-tex\">$a+b+c=2$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-20 09:21:36","option_type":"txt","len":0},{"id":"5926","post_id":"8058","mon_id":"1159285","chapter_id":"1159380","question":"<p>T&iacute;nh t&iacute;ch ph&acirc;n&nbsp;<span class=\"math-tex\">$\\int\\limits_0^1e^{3x+1}dx$<\/span>&nbsp;b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{3}(e^4+e)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$e^3-e$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{3}(e^4-e)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$e^4-e$<\/span>"],"correct":"3","level":"2","hint":"<p>S\u1eed d\u1ee5ng c&ocirc;ng th\u1ee9c t&iacute;nh t&iacute;ch ph&acirc;n&nbsp;<span class=\"math-tex\">$\\int\\limits_c^de^{ax+b}dx=\\dfrac{1}{a}.e^{ax+b}\\bigg|_c^d$<\/span><\/p>","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{1}{3}(e^4-e)$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\int\\limits_0^1e^{3x+1}dx$<\/span>&nbsp;<span class=\"math-tex\">$=\\dfrac{1}{3}.e^{3x+1}\\bigg|_0^1$<\/span>&nbsp;<span class=\"math-tex\">$=\\dfrac{1}{3}.(e^4-e)$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-20 09:33:00","option_type":"math","len":0},{"id":"5928","post_id":"8058","mon_id":"1159285","chapter_id":"1159380","question":"<p>T&iacute;nh&nbsp;<span class=\"math-tex\">$I=\\int\\limits_0^1\\dfrac{e^x}{2^x}dx$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$I=\\dfrac{e}{2}-1$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$I=\\dfrac{1}{1-\\ln2}.\\bigg(\\dfrac{e}{2}-1\\bigg)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$I=\\dfrac{1}{1-\\ln2}.\\bigg(\\dfrac{e}{2}+1\\bigg)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$I=\\dfrac{1}{1-\\ln2}.\\dfrac{e}{2}$<\/span>"],"correct":"2","level":"2","hint":"<p>Bi\u1ebfn \u0111\u1ed5i&nbsp;<span class=\"math-tex\">$\\dfrac{e^x}{2^x}=\\bigg(\\dfrac{e}{2}\\bigg)^x$<\/span>.<\/p>","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$I=\\dfrac{1}{1-\\ln2}.\\bigg(\\dfrac{e}{2}-1\\bigg)$<\/span><\/span><\/p><p><span class=\"math-tex\">$I=\\int\\limits_0^1\\dfrac{e^x}{2^x}dx=\\int\\limits_0^1\\bigg(\\dfrac{e}{2}\\bigg)^xdx=\\dfrac{1}{1-\\ln2}.\\bigg(\\dfrac{e}{2}\\bigg)^x\\bigg|_0^1$<\/span>&nbsp;<span class=\"math-tex\">$=\\dfrac{1}{1-\\ln2}.\\bigg(\\dfrac{e}{2}-1\\bigg)$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-20 09:48:35","option_type":"math","len":0}]}