7.4 Integration of Rational Functions by the Method of Partial Fractions

1.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-1.html

-x/(x^2 - 2*x + 1) + 2*log(x - 1) - log(x)

2.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-2.html

1/2*log(x-1)+1/2*log(x+1)-log(x) 

3.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-3.html

2/3*log(x - 5) + 1/3*log(x + 1)

4.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-4.html

-4/(x^2 - 4) + 3*log(x - 2) + 2*log(x + 2)

5.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-5.html

2/3*arctan(1/2*x) - 1/3*arctan(x)

6.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-6.html

1/2*x^2 + 2*x + 3/2*log(x - 1) - 1/2*log(x + 1)

7.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-7.html

1/2*log(x^2 + 1) + log(x)

8.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-8.html

1/3*sqrt(3)*arctan(1/3*(2*x-1)*sqrt(3))+1/3*log(x+1)-1/6*log(x^2-x+1)

9.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-9.html

-5/(x - 3) + 3*log(x - 3)

10.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-10.html

-1/6 * sqrt(3) * arctan(1/3*(2*x-1)*sqrt(3)) - 1/6 * sqrt(3) * arctan(1/3*(2*x+1) * sqrt(3)) + 1/6 * log(x-1) - 1/6 * log(x+1) + 1/12 * log(x^2-x+1) - 1/12 * log(x^2+x+1)

11.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-11.html

-1/8 * sqrt(2) * log(x^2-sqrt(2) * x+1) + 1/8 * sqrt(2) * log(x^2+sqrt(2) * x+1) + 1/4 * sqrt(2) * arctan(1/2*(2*x-sqrt(2)) * sqrt(2)) + 1/4 * sqrt(2) * arctan(1/2 * (2*x + sqrt(2)) * sqrt(2))

12.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-12.html

3/5*arctan(1/3*x) - 2/5*arctan(1/2*x)

13.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-13.html

-1/2*x/(x^2 + 1) + 1/2*arctan(x)

14.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-14.html

-1/4*(x-1)/(x^2+1)+1/4*log(x-1)-1/8*log(x^2+1)-1/2*arctan(x)

15.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-15.html

-(14*x^2 - 34*x + 19)/(x^3 - 4*x^2 + 5*x - 2) - 14*log(x - 2) + 14*log(x - 1)

16. .

http://matrix.skku.ac.kr/cal-lab/cal-7-4-16.html

-4*log(x + 1) + 13/2*log(2*x + 3)

17.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-17.html

sqrt(x^2 + 9) - 3*arcsinh(3/abs(x))

18.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-18.html

-1/2*(12*x^3 - 18*x^2 + 4*x + 1)/(x^4 - 2*x^3 + x^2) - 6*log(x - 1) + 6*log(x)

19.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-19.html

A^3*log(x) + 1/6*(2*x^(3*n) + 18*x^n*A^2 + 9*A*x^(2*n)) / n

20.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-20.html

-1/9*pi*sqrt(3) + 1/3*log(2) + 1/2

21.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-21.html

1/2*log(x^2 + 4) + log(x) - 1/2*arctan(1/2*x)

22.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-22.html

1/2*x/(x^2 + 1) + 1/2*arctan(x)

23.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-23.html

1/3*sqrt(3)*log((sqrt(x + 2) - sqrt(3))/(sqrt(x + 2) + sqrt(3)))1/3*sqrt(3)*log((sqrt(x + 2) - sqrt(3))/(sqrt(x + 2) + sqrt(3)))

24.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-24.html

4*sqrt(-(x + 2)/(x - 2))/((x + 2)/(x - 2) - 1) + 4*arctan(sqrt(-(x +2)/(x - 2)))

25.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-25.html

-6*x^(1/6) - 3*log(x^(1/6) - 1) + 3*log(x^(1/6) + 1)

26.

.

27.

http://matrix.skku.ac.kr/cal-lab/cal-7-4-27.html

-1/2*sqrt(2)*arcsinh(x/abs(x) + 2/abs(x))