Answers edited by Frederico Guizini S.

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• How do you integrate `int sec^2x/(1+tanx)^3` using substitution?
  
• Question #5698e
  
• How do you integrate `int xroot3(4+x^2)` from [0,2]?
  
• How do you find the area of the common interior of `r=4sintheta, r=2`?
  
• How do you evaluate `int (x^3 + 2x^2 + 5x - 2)/(x^2 + 2x + 2)^2 dx`?
  
• How do you integrate `[6/(x-3)^4*(x^2-4x+4)]` using partial fractions?
  
• What's the derivative of `arctan [(1-x)/(1+x)]^(1/2)`?
  
• How do you integrate `(6x^2-x-1)/(3x-1)` using partial fractions?
  
• How do you integrate `ln (x^2+14x+24)dx`?
  
• Question #25ffa
  
• How do you find critical point for this equation `f(x,y)=6x^7+7y^2+8xy+9`?
  
• How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y= x, `y = sqrt(x)`; about x = 2?
  
• How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region `y= sqrt x`, `y=0` and `y=(x-3)/2` rotated about the x-axis?
  
• How do you find the antiderivative of `int sqrt(9+4x^2) dx`?
  
• How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for `f(x) = 3x^4 + 16x^3 + 24x^2 + 32`?
  
• How do you differentiate `y=r/sqrt(r^2+1)`?
  
• What is the equation of the line tangent to `f(x)=(e^x-sinx)/(x-xcosx)` at `x=pi/3`?
  
• How do you integrate? dx/sqrt(4x^2-8x-1)
  
• The region under the curves `x=0, x=y-y^4` is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
  
• How do you differentiate `f(x)= e^x/(xe^(x) -x )` using the quotient rule?
  
• What is the derivative of `f(t) = ((lnt)^2-t, sec(1-t) )`?
  
• What is `int1/(x^2-5)`?
  
• How do you find the critical points for `f(x) = 2x^(2/3) - 5x^(4/3)` and the local max and min?
  
• I really don't understand this calculus 2 problem?