7.6 Integration Using Tables

1. .

        http://matrix.skku.ac.kr/cal-lab/cal-7-6-1.html

-1/6*sqrt(-3*x^2 + 7)*x + 7/18*sqrt(3)*arcsin(1/7*sqrt(21)*x)


2. .

        http://matrix.skku.ac.kr/cal-lab/cal-7-6-2.html

5*(x^4 - 12*x^2 + 24)*sin(x) - (x^5 - 20*x^3 + 120*x)*cos(x)


3.  

        http://matrix.skku.ac.kr/cal-lab/cal-7-6-3.html

-1/96*sin(4*x)^3 + 1/16*x - 1/128*sin(8*x)


4. .

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

1/3*(x^2 - 4*x + 7)^(3/2) + sqrt(x^2 - 4*x + 7)*x - 2*sqrt(x^2 – 4*x+7) + 3*arcsinh(1/3*(x – 2)*sqrt(3))1/3*(x^2 - 4*x + 7)^(3/2) + sqrt(x^2 - 4*x + 7)*x - 2*sqrt(x^2 - 4*x + 7) + 3*arcsinh(1/3*(x - 2)*sqrt(3))


5. .

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

-1/48*(15*sin(x)^5 - 40*sin(x)^3 + 33*sin(x))/(sin(x)^6 - 3*sin(x)^4 +3*sin(x)^2 – 1) - 5/32*log(sin(x) - 1) + 5/32*log(sin(x) + 1)


6. .

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

1/4*x^4*arctan(3*x) - 1/36*x^3 + 1/108*x - 1/324*arctan(3*x)


7. .

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

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


8. .

        http://matrix.skku.ac.kr/cal-lab/cal-7-6-8.html

1/4*(-3*e^(2*x) + 2)^(3/2)*e^x + 3/4*sqrt(-3*e^(2*x) + 2)*e^x +1/2*sqrt(3)*arcsin(1/2*sqrt(6)*e^x)


9. .

        http://matrix.skku.ac.kr/cal-lab/cal-7-6-9.html

-log(log(x) + 1) + log(log(x))


10. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-6-10.html

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


11. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-6-11.html

1/13*(3*sin(3*x) + 2*cos(3*x))*e^(2*x)


12. .

         http://matrix.skku.ac.kr/cal-lab/cal-7-6-12.html

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