A series of integral based questions?

  1. #\intx^5\ln(x)dx#
    My answer: #x^6/6(\ln(x)-1/6)+C#
  2. #\int\sec^3(x)\tan(x)dx#
    My answer: #1/3\sec^3(x)+C#
  3. #\int(x^3)/(x^2+1)dx#
    My answer: #x^2/2-2\ln|x^2+1|+C#
  4. #\int(5x)/(x^2-3x)dx#
    My answer: #5\ln|x-3|+C#
  5. Find the area of the region bounded by #y=4-x^2# and #y=2x+1#.
    My answer: #27/3#
  6. Find the volume of the region bounded by #y=x^3#, #y=0#, and #x=3#, revolved around the y-axis.
    My answer: #(243\pi)/5#
  7. Approximate #\int_2^4\sqrt(x-2)dx# using the Trapezoidal rule, rounding to 4 decimal places.
    My answer: #\approx1.8195#
  8. #\int_1^\infty(\tan^-1(x))/(x^2+1)dx#
    My answer: divergent (#\infty#) ?