kill(all)$

van=facebook.com/LearningCalculus$

     Problems 1 - 6

integrate(x/sqrt(1-x^4),x)+C;

integrate(%e^x/sqrt(4+%e^(2*x)),x)+C;

integrate(%pi*x/2,x)+C;

integrate(1/sqrt(x^2-3),x)+C;

integrate(x/%e^(-5*x),x,0,1)+C;

integrate(1/sec(sqrt(x)),x,1,4)+C;

    Problems 7 - 12

integrate(asin(x),x,0,1/2)+C;

integrate(x/sec(x),x,1,2);

integrate(ln(x^2+1),x,0,2) = x*log(x^2+1)-2*x+2*atan(x);

integrate(cos(sqrt(x)),x)+C;

integrate(e^sqrt(x),x)+C;

integrate(x*%e^(-x),x)+C;

    Problems 13 - 18

integrate(tan(x)^4,x)+C;

integrate(sin(x)^2*cos(x)^2,x)+C;

integrate(sin(x)^3*cos(x)^3,x)+C;

integrate(sin(2*x)^3*cos(2*x)^2,x)+C;

integrate(sqrt(tan(x))*sec(x)^4,x)+C;

integrate(tan(x)*sec(x)^(3/2),x)+C;

     Problems 19 - 24

integrate(%e^x*sqrt(1-%e^(2*x)),x)+C;

integrate(x^3*sqrt(16-x^2),x,0,4);

integrate(1/(x^2-4*x+13),x);

integrate(1/sqrt(8+2*x-x^2),x);

integrate(1/(2*x^2+4*x+7),x);

integrate(1/sqrt(4*(4-x)),x,0,1);

     Problems 25 - 30

integrate(%e^x/sqrt(1+%e^x+%e^(2*x)),x)+C;

integrate(1/sqrt(2*x-x^2),x)+C;

integrate((x^2+2)/(x+2),x)+C;

integrate((x^2-4)/(x-1),x)+C;

integrate(1/(x^3+x),x)+C;

integrate((2*x^2-2*x-1)/(x^3-x^2),x)+C;

     Problems 31- 36

integrate(1/(x^3+x),x)+C;

integrate(sin(3*x)*cos(2*x),x)+C;

integrate(sqrt(x)/(1+x^(1/3)),x)+C;

integrate(sqrt(1+%e^x),x)+C;

integrate(1+sin(x)+cos(x),x)+C;

integrate(1/(2+sin(x)),x)+C;

    Problems 37 - 42

integrate(1/(sin(x)+tan(x)),x);

integrate(1/(4*sin(x)-3*cos(x)),x);

integrate(cos(x)/(2-cos(x)),x);

integrate(1/(1+x^2),x,minf,inf);

integrate(1/(1-x),x,a,b);

integrate(1/(x-2)^(2/3),x,1,4);

     Problems 43 - 45

integrate(1/(x-1)^2,x,a,b);

integrate(1/(sqrt(x)*(x+1)),x,0,inf);

fullratsimp(factor(integrate(sin(x)/sqrt(1-x),x,0,1)));