Answers edited by Tom

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• How do you demonstrate that, if #(df)/(dr)= (dg)/(dy)#, then #(df)/(dr)= (dg)/(dy) = K # where K is a constant ?
  
• How do you integrate #x^2/(x^3+1)#?
  
• What is the integral of #ln(sqrt(x))#?
  
• How do you solve #3^(2x) = 81#?
  
• What is the use of iso, sec & tert in IUPAC naming of organic compounds?
  
• How do you integrate #((cosx)^3 sinx )/(4sqrt{1-(cosx)^4})dx#?
  
• How do integrate #int e^(cos)(t) (sin 2t) dt# between a = 0, #b = pi#?
  
• How do you integrate #cscxcot^4xdx#
  
• How do you show whether the improper integral #int dx / [(lnx)^2]# converges or diverges from e to infinity?
  
• How do you find the determinant of #((0, 1, 2, 3), (0, 0, 2, 0), (3, 10, 12, 20), (0, 0, 0, 4))#?
  
• How do you find #int 1-tan^2xdx#?
  
• How do you integrate #int 1/sqrt(e^(2x)+12e^x-45)dx# using trigonometric substitution?
  
• What is the derivative of #y = sin(sin(sinx))#?
  
• How do you find the integral of #xe^(x/2)dx #?
  
• How do you evaluate the integral from 0 to #pi/4# of #(1 + cos^2 x) / (cos^2 x) dx#?
  
• What is the derivative of #e^((lnx)^2)#?
  
• How do you integrate #x^3/((x^2+5)^2)#?
  
• Question #d453a
  
• What is the equation of the line perpendicular to #y=-9/7x # that passes through # (3,7) #?
  
• How do you find the Integral of #(1-x^2)^(3/2)/ (x^6)#?
  
• How do you find integral of #((secxtanx)/(secx-1))dx#?
  
• How do you integrate #int x sin sqrtx dx # using integration by parts?
  
• How do you find the integral of #(1+ tan^2x)sec^2xdx#?
  
• How do you factor the trinomial # 49x^2 − 8x + 16#?
  
• How do you find the integral from zero to #pi/2# for #cos^4(2x)dx#?
  
• How do you find the antiderivative of #secx / (1+tan^2x)#?
  
• How do you integrate #int ( x^2 + 2 ) / (x+2) dx# using partial fractions?
  
• If #f(x) = sin x#, what is #f''(pi/6)#?
  
• How do you factor #y=4x^3+12x^2-16x-48 #?
  
• Question #7a7ca
  
• How do you find the integral of # 1/sin^2(x)#?
  
• How do you integrate #(1/x^2)(sin(2lnx)) dx #?
  
• Question #694f3
  
• How do you verify the identity #sin(pi/2 + x) = cosx#?
  
• Please find the value for this integration. What is the answer?
  
• How do you find the exact value of #cos[arctan(-8/15)]#?
  
• Does #a_n=x^n/(n!) # converge for any x?