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Indefinite Integrals

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  1. 251.If _0^/3√2k,d=1-1√2, (k>0) then the value of k is:
  2. 252.If x^5e^-4x^3,dx=148e^-4x^3f(x)+C, where C is a constant of integration, then f(x) is equa…
  3. 253.A value of such that _^+1(dx)/((x+)(x++1))=_e98 is:
  4. 254.The integral (2x^3-1)/(x^4+x),dx is equal to : (Here C is a constant of integration)
  5. 255.Let (0,/2) be fixed.
  6. 256.If (dx)/((x^2-2x+10)^2)=A^-1(x-13)+f(x)x^2-2x+10+C where C is a constant of integration, t…
  7. 257.If f(x) is a non-zero polynomial of degree four, having local extreme points at x=-1,0,1; …
  8. 258.The integral ^2/3x^4/3x,dx is equal to: (Here C is a constant of integration)
  9. 259.If e^ x( x x,f(x)+( x x+^2x))dx=e^ xf(x)+C, then a possible choice of f(x) is:
  10. 260.5x2 x2,dx is equal to : (where c is a constant of integration.)
  11. 261.If dxx^3(1+x^6)^2/3=xf(x)(1+x^6)^1/3+C, where C is a constant of integration, then the fun…
  12. 262.If x^5e^-x^2,dx=g(x)e^-x^2+c, where c is a constant of integration, then g(-1) is equal to…
  13. 263.Let f:RR be a continuously differentiable function such that f(2)=6 and f'(2)=148.
  14. 264.If _0^/2 x2( x)/( x+ x),dx=m(+n), then m n is equal to :
  15. 265.The value of _0^2[2x(1+3x)],dx, where [t] denotes the greatest integer function, is:
  16. 266.The integral _/6^/3^2/3x^4/3x,dx is equal to:
  17. 267.The value of _0^/2(^3x)/( x+ x),dx is:
  18. 268.The value of the integral _0^1x^-1(1-x^2+x^4)dx is:
  19. 269.If f:RR is a differentiable function and f(2)=6, then _x2_6^f(x)2t,dtx-2 is:
  20. 270.If f(x)=2-x x2+x x and g(x)=_ex, (x>0) then the value of the integral _-/4^/4g(f(x)),dx is…
  21. 271.Let f(x) = _0^x g(t),dt, where g is a non-zero even function.
  22. 272._n [(n+1)^1/3n^4/3 + (n+2)^1/3n^4/3 + + (2n)^1/3n^4/3] is equal to:
  23. 273.The integral (^2x^2x)/((^5x + ^3x^2x + ^3x^2x + ^5x)^2),dx is equal to:
  24. 274.If x1+ x + ^2x,dx = x - KA^-1K x + 1A + C, (C is a constant of integration), then the orde…
  25. 275.If f(x-4x+2) = 2x+1, (x R - 1,-2), then f(x),dx is equal to (where C is a constant of inte…
  26. 276.2x+5√7-6x-x^2,dx = A√7-6x-x^2 + B^-1(x+34) + C (where C is a constant of integration), the…
  27. 277.The value of _-/2^/2 ^2x1+2^x,dx is:
  28. 278.If f(x) = _0^x t( x - t),dt then
  29. 279.The value of integral _/4^3/4 x1+ x,dx is
  30. 280.If I_1 = _0^1 e^-x^2x,dx; I_2 = _0^1 e^-x^2^2x,dx and I_3 = _0^1 e^-x^3,dx; then
  31. 281.The value of the integral _-/2^/2 ^4x [(2+ x2- x)+1]dx is
  32. 282.If f(3x-43x+4) = x+2, x -43, and f(x),dx = A|1-x| + Bx + C, then the ordered pair (A,B) is…
  33. 283.The integral √1+2 x( x+ x),dx, 0 < x < 2 is equal to: (where C is a constant of integratio…
  34. 284.The integral _/4^3/4 dx1+ x is equal to:
  35. 285.Let I_n = ^nx,dx, (n>1).
  36. 286.If _1^2 dx(x^2-2x+4)^3/2 = kk+5 then k is equal to:
  37. 287.The integral _/12^/4 8 2x( x + x)^3,dx equals:
  38. 288.If _n 1^a+2^a++n^a(n+1)^a-1[(na+2)++(na+n)] = 160 for some positive real number a, then a …
  39. 289.If dx^3x√2 2x = ( x)^A + C( x)^B + k, where k is a constant of integration, then A+B+C equ…
  40. 290.The integral dx(1+ x)x-x^2 is equal to: (where C is a constant of integration)
  41. 291.The integral 2x^12+5x^9(x^5+x^3+1)^3,dx is equal to:
  42. 292.For x R, x 0, if y(x) is a differentiable function such that x_1^x y(t),dt = (x+1)_1^x ty(…
  43. 293.The value of the integral _4^10 [x^2],dx[x^2-28x+196]+[x^2], where [x] denotes the greates…
  44. 294.If 2_0^1 ^-1x,dx = _0^1 ^-1(1-x+x^2),dx, then _0^1 ^-1(1-x+x^2),dx is equal to:
  45. 295._n [(n+1)(n+2) 3nn^2n]^1/n is equal to:
  46. 296.If (t+√1+t^2)√1+t^2,dt = 12(g(t))^2+C, where C is a constant, then g(b) is equal to: (Here…
  47. 297.The integral dxx^2(x^4+1)^3/4 equals:
  48. 298.The integral dx(x+1)^3/4(x-2)^5/4 is equal to:
  49. 299.The integral _2^4 x^2 x^2+(36-12x+x^2),dx is equal to
  50. 300.Let f: R R be a function such that f(2-x) = f(2+x) and f(4-x) = f(4+x), for all x R and _0…