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Indefinite Integrals

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  1. 201.If U_n=_r=1^n(1+(r^2)/(n^2))^r, then _n(U_n)^-4/n^2 is equal to
  2. 202._6^16(_ex^2)/(_ex^2+_e(x^2-44x+484)),dx is equal to
  3. 203.The value of the integral _0^1( x,dx)/((1+x)(1+3x)(3+x)) is
  4. 204.The value of _-1/√2^1/√2[((x+1)/(x-1))^2+((x-1)/(x+1))^2-2]^1/2dx is
  5. 205.The value of _n1n_r=0^2n-1(n^2)/(n^2+4r^2) is
  6. 206.If the value of the integral _0^5x+[x]e^x-[x],dx= e^-1+, where ,R, 5+6=0 and [x] denotes t…
  7. 207.The function f(x), that satisfies the condition f(x)=x+_0^/2 x y,f(y),dy, is
  8. 208.The integral dx(x+4)^8/7(x-3)^6/7 is equal to: (where C is a constant of integration)
  9. 209.If (d)/(^2(2+2))=+2_e|f()|+C where C is a constant of integration, then the ordered pair (…
  10. 210.If x,dx^3x(1+^6x)^2/3=f(x)(1+^6x)^1/+c where c is a constant of integration, then f(3) is …
  11. 211.If for all real triplets (a,b,c), f(x)=a+bx+cx^2; then _0^1f(x),dx is equal to:
  12. 212.The value of _0^2(x^8x)/(^8x+^8x),dx is equal to:
  13. 213.If I=_1^2dx√2x^3-9x^2+12x+4, then:
  14. 214.If f(a+b+1-x)=f(x), for all x, where a and b are fixed positive real numbers, then 1a+b_a^…
  15. 215.The value of for which 4_-1^2 e^-|x|dx=5, is :
  16. 216.If _1 and _2 be respectively the smallest and the largest values of in (0,2)- which satisf…
  17. 217.Let a function f:[0,5]R be continuous, f(1)=3 and F be defined as: F(x)=_1^xt^2g(t),dt, wh…
  18. 218._x1_0^(x-1)^2t(t^2),dt(x-1)(x-1)
  19. 219.If (e^2x+2e^x-e^-x-1)e^(e^x+e^-x),dx=g(x)e^(e^x+e^-x)+c, where c is a constant of integrat…
  20. 220.If ()/(5+7-2^2),d=A_e|B()|+C, where C is a constant of integration, then B()A can be:
  21. 221.The integral (x^2)/((x x+ x)^2),dx is equal to (where C is a constant of integration):
  22. 222.Let f(x)=( x)/((1+x)^2),dx (x0).
  23. 223.If ^-1 x√1+x,dx=A(x)^-1( x)+B(x)+C, where C is a constant of integration, then the ordered…
  24. 224.The integral _1^2e^x x^x(2+_ex),dx equals:
  25. 225.If I_1=_0^1(1-x^50)^100dx and I_2=_0^1(1-x^50)^101dx such that I_2= I_1 then equals to :
  26. 226.The value of _-/2^/211+e^ x,dx is:
  27. 227.Let f(x)=|x-2| and g(x)=f(f(x)), x[0,4].
  28. 228.The integral _/6^/3^3x^23x(2^2x^23x+3 x6x)dx is equal to :
  29. 229.Let x and [x] denote the fractional part of x and the greatest integer x respectively of a…
  30. 230._-^|-|x||,dx is equal to :
  31. 231.If the value of the integral _0^1/2x^2(1-x^2)^3/2,dx is k6, then k is equal to:
  32. 232.The integral _0^2||x-1|-x|,dx is equal to _______.
  33. 233.Let [t] denote the greatest integer less than or equal to t.
  34. 234.For x^2 n+1, n N (the set of natural numbers), the integral (x[2(x^2-1)-2(x^2-1)])/(2(x^2-…
  35. 235.If f(x)=(5x^8+7x^6)/((x^2+1+2x^7)^2),dx, (x0) and f(0)=0, then the value of f(1) is:
  36. 236.The integral (_ex),dx is equal to : (where C is a constant of integration)
  37. 237.The integral 3x^13+2x^11(2x^4+3x^2+1)^4,dx is equal to: (where C is a constant of integrat…
  38. 238.If √1-x^2x^4,dx=A(x)(√1-x^2)^m+C, for a suitable chosen integer m and a function A(x), whe…
  39. 239.If x+1√2x-1,dx=f(x)√2x-1+C, where C is a constant of integration, then f(x) is equal to:
  40. 240.Let n2 be a natural number and 0<<2.
  41. 241._n[(n)/(n^2+1^2)+(n)/(n^2+2^2)+(n)/(n^2+3^2)++15n] is equal to :
  42. 242.Let f and g be continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=4, then…
  43. 243.The integral _1^e( xe^2x-e^xx)_ex,dx is equal to :
  44. 244.The value of the integral _-2^2(2x)/([ x]+12),dx (where [x] denotes the greatest integer l…
  45. 245.The integral _/6^/4(dx)/(2x(^5x+^5x)) equals:
  46. 246.Let I=_a^b(x^4-2x^2),dx.
  47. 247.If _0^xf(t),dt=x^2+_x^1t^2f(t),dt, then f'(1/2) is:
  48. 248.The value of _-/2^/2(dx)/([x]+[ x]+4), where [t] denotes the greatest integer less than or…
  49. 249.The value of _0^| x|^3,dx is:
  50. 250.Let f be a differentiable function from R to R such that |f(x)-f(y)|2|x-y|^3/2, for all x,…