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)