ThanhTam
14-01-2009, 09:53 PM
Tóm tắt lý thuyết:
[Only registered and activated users can see links]
Bài tập giải mẫu:
1. Tính tích phân:
[Only registered and activated users can see links] %7B2x%5E%7B2%7D+%2B+2x+%2B+3%7D%7D+%5C%2Cdx+&bg=ffffff&fg=333333&s=0
Ở đây, ta gặp dạng tích phân bậc tử bé hơn bậc mẫu 1 bậc. Do đó, ta thêm bớt ở tử số để xuất hiện biểu thức là đạo hàm của mẫu. Bài này cần xuất hiện 4x + 2 ở tử số. Ta có:
[Only registered and activated users can see links] 7D%7B+%5Cdfrac%7B%284x+%2B+2%29+%2B+8%7D%7B2x%5E%7 B2%7D+%2B+2x+%2B+3%7D%7D+%5C%2Cdx+&bg=ffffff&fg=333333&s=0
Hay:
[Only registered and activated users can see links] 5Cint+%7B+%5Cdfrac%7B%284x+%2B+2%29%7D%7B2x%5E%7B2 %7D+%2B+2x+%2B+3%7D%7D+%5C%2Cdx%7D+%2B+%7B%5Cint+% 7B+%5Cdfrac%7B4%7D%7B2x%5E%7B2%7D+%2B+2x+%2B+3%7D% 7D+%5C%2Cdx%7D&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+%7B%5C int+%7B+%5Cdfrac%7B2%7D%7Bx%5E%7B2%7D+%2B+x+%2B+3% 2F2%7D%7D+%5C%2Cdx%7D&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+%7B%5C int+%7B+%5Cdfrac%7B2%7D%7B%28x%2B1%2F2%29%5E%7B2%7 D+%2B+5%2F4%7D%7D+%5C%2C+dx%7D&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+2.%7B+ %5Cdfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%7D.%7Barctg%7B %28%7B+%5Cdfrac%7Bx%2B1%2F2%7D%7B+%5Cdfrac%7B%5Csq rt%7B5%7D%7D%7B2%7D%7D%7D%29%7D%7D+%2B+C+&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+%7B+%5 Cdfrac%7B4.%7B%5Csqrt%7B5%7D%7D%7D%7B5%7D%7D.%7Bar ctg%7B%28%7B+%5Cdfrac%7B%7B%282x%2B1%29%7D.%7B%5Cs qrt%7B5%7D%7D%7D%7B5%7D%7D%29%7D%7D+%2B+C+&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links]
Bài tập giải mẫu:
1. Tính tích phân:
[Only registered and activated users can see links] %7B2x%5E%7B2%7D+%2B+2x+%2B+3%7D%7D+%5C%2Cdx+&bg=ffffff&fg=333333&s=0
Ở đây, ta gặp dạng tích phân bậc tử bé hơn bậc mẫu 1 bậc. Do đó, ta thêm bớt ở tử số để xuất hiện biểu thức là đạo hàm của mẫu. Bài này cần xuất hiện 4x + 2 ở tử số. Ta có:
[Only registered and activated users can see links] 7D%7B+%5Cdfrac%7B%284x+%2B+2%29+%2B+8%7D%7B2x%5E%7 B2%7D+%2B+2x+%2B+3%7D%7D+%5C%2Cdx+&bg=ffffff&fg=333333&s=0
Hay:
[Only registered and activated users can see links] 5Cint+%7B+%5Cdfrac%7B%284x+%2B+2%29%7D%7B2x%5E%7B2 %7D+%2B+2x+%2B+3%7D%7D+%5C%2Cdx%7D+%2B+%7B%5Cint+% 7B+%5Cdfrac%7B4%7D%7B2x%5E%7B2%7D+%2B+2x+%2B+3%7D% 7D+%5C%2Cdx%7D&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+%7B%5C int+%7B+%5Cdfrac%7B2%7D%7Bx%5E%7B2%7D+%2B+x+%2B+3% 2F2%7D%7D+%5C%2Cdx%7D&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+%7B%5C int+%7B+%5Cdfrac%7B2%7D%7B%28x%2B1%2F2%29%5E%7B2%7 D+%2B+5%2F4%7D%7D+%5C%2C+dx%7D&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+2.%7B+ %5Cdfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%7D.%7Barctg%7B %28%7B+%5Cdfrac%7Bx%2B1%2F2%7D%7B+%5Cdfrac%7B%5Csq rt%7B5%7D%7D%7B2%7D%7D%7D%29%7D%7D+%2B+C+&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] %7Bln%282x%5E%7B2%7D+%2B+2x+%2B+3%29%7D+%2B+%7B+%5 Cdfrac%7B4.%7B%5Csqrt%7B5%7D%7D%7D%7B5%7D%7D.%7Bar ctg%7B%28%7B+%5Cdfrac%7B%7B%282x%2B1%29%7D.%7B%5Cs qrt%7B5%7D%7D%7D%7B5%7D%7D%29%7D%7D+%2B+C+&bg=ffffff&fg=333333&s=0