7.5 Guidelines for Integration

1. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-1.html

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


2. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-2.html

2*(sqrt(x + 5) - 1)*e^(sqrt(x + 5))


3. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-3.html

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


4. .

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

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


5. .

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


1/315*(63*cos(x)^4 - 90*cos(x)^2 + 35)/cos(x)^9


6. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-6.html

-1/15*(5*tan(x)^2 + 3)/tan(x)^5


7. .

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

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


8. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-8.html

6*x^(1/6) - 6*arctan(x^(1/6))


9. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-9.html

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

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


 10. .

http://matrix.skku.ac.kr/cal-lab/cal-7-5-10.html

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


11. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-5-11.html

-20/(x + 1) + x^3 - 7/2*x^2 + 20*x - 34*log(x + 1)


12. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-12.html

4*(x^(3/4) - 3*sqrt(x) + 6*x^(1/4) - 6)*e^(x^(1/4))


13. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-13.html

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


14. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-14.html

1/2*sqrt(-x^2 + 3*x - 2)*x - 3/4*sqrt(-x^2 + 3*x - 2) + 1/8*arcsin(2*x -3)


15. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-15.html

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


16. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-16.html

-1/12*x*cos(3*x) - 1/4*x*cos(x) + 1/36*sin(3*x) + 1/4*sin(x)


17. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-17.html

5/11*(x + 1)^(11/5) - 5/6*(x + 1)^(6/5)


18. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-18.html

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


19. .

          http://matrix.skku.ac.kr/cal-lab/cal-7-5-19.html

-1/2*arctan(sqrt(-x^4 + 3)/x^2)