[+(-)/(2)log(x-3)+c],[int(3x+5)/(x^(3)-x^(2)-x+1)dx]

int(x ln x)/((x^(2)-1)^((3)/(2)))dx

" (3) "int(dx)/(x(1+log (x))^(2))

Match the following. I. int (1)/(9+x^(2))dx= " " a) (1)/(6) log |(3+x)/(3-x)|+c II. int (1)/(x^(2)-9)dx= " " b) (1)/(6) log |(3-x)/(3+x)|+c III. int (1)/(9-x^(2))dx= " "c)(1)/(3)"Tan"^(-1)(x)/(3)+c

int_(2)^(3)((3+log x)^(2))/(x)dx

int_(1)^(3)(log x)/((x+1)^(2))dx

int_(1)^(3)(log x)/((x+1)^(2))dx

If int f(x)dx=psi(x), then int x^(5)f(x^(3))dxint x^(5)f(x^(3))dx(1)/(3)x^(3)psi(x^(3))-3int x^(3)psi(x^(3))dx+C(2)(1)/(3)x^(3)psi(x^(3))-int x^(3)psi(x^(3))dx+C(3)(1)/(3)x^(3)psi(x^(3))-int x^(3)psi(x^(3))dx+C(4)(1)/(3)[x^(3)psi(x^(3))-int x^(2)psi(x^(3))dx]+C

int((2+log x)^(3))/(x)dx

int_(1)^(3)(log x)^2/(x)dx