"Subtask 1\n\n´int 1/(x^2-1) dx´\n\nFactor ´-1´ from the denominator:\n´= - int 1/(1-x^2) dx´\n\nThe integral of ´1/(1-x^2)´ is ´tanh^(-1)(x)´:\n´= -tanh^(-1)(x) + "constant"´\n\nFor ´x in RR ^^ -1 < x < 1´this is equivalent to:\n´= 1/2 (log(1-x)-log(x+1)) + "constant"´\n\n\nSubtask 2\n\n´int sin(8 x+4) dx´\n\nFor the integrand ´sin(8 x+4)´, substitute ´u = 8 x + 4´ and ´du = 8 dx´:\n´= 1/8 int sin(u) du´\n\nThe integral of ´sin(u)´ is ´-cos(u)´:\n´= -(cos(u))/8 + "constant"´\n\nSubstitute back for ´u = 8 x+4´:\n´= -1/8 cos(8 x+4) + "constant"´\n\n\nSubtask 3\n\n´int e^x x^2 dx´\n\nFor the integrand ´e^x x^2´, integrate by parts, ´int f dg = f g- int g df´, where ´f = x^2´, ´dg = e^x dx´, ´df = 2 x dx´, ´g = e^x´:\n´= e^x x^2-2 int e^x x dx´\n\nFor the integrand ´e^x x´, integrate by parts, integral ´f dg = f g- int g df´, where ´f = x´, ´dg = e^x dx´, ´df = dx´, ´g = e^x´:\n´= e^x x^2-2 e^x x+2 int e^x dx´\n\nThe integral of e^x is e^x:\n´= e^x x^2-2 e^x x+2 e^x + "constant"´\n\n´= e^x (x^2-2 x+2) + "constant"´"