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Indefinite Integrals

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  1. 351._n[1n^2^21n^2+2n^2^24n^2++1n^2 1] equals:
  2. 352.dx x- x is equal to:
  3. 353.If x(x-),dx = Ax+B(x-)+C, then value of (A,B) is:
  4. 354.If f(x) = e^x1+e^x, I_1 = _f(-a)^f(a) xgx(1-x),dx and I_2 = _f(-a)^f(a) gx(1-x),dx, then t…
  5. 355.If _0^ xf( x),dx = A_0^/2 f( x),dx, then A is:
  6. 356.The value of I = _0^/2 ( x+ x)^2√1+2x,dx is:
  7. 357._n _r=1^n 1ne^r/n is:
  8. 358.The value of the integral I = _0^1 x(1-x)^n,dx is:
  9. 359.Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satis…
  10. 360.If f(a+b-x)=f(x) then _a^b xf(x),dx is equal to:
  11. 361.The value of _x0 _0^x^2^2t,dtx x is:
  12. 362.If f(y)=e^y, g(y)=y; y>0 and F(t) = _0^t f(t-y)g(y),dy, then:
  13. 363._n 1^4+2^4+3^4++n^4n^5 - _n 1^3+2^3+3^3++n^3n^5
  14. 364.f(x) and g(x) are two differentiable functions on [0,2] such that f''(x)-g''(x)=0, f'(1)=2…
  15. 365._-^ 2x(1+ x)1+^2x,dx is:
  16. 366._0^2 [x^2],dx is:
  17. 367.I_n = _0^/4 ^nx,dx then _n n[I_n+I_n+2] equals:
  18. 368._0^10 | x|,dx is:
  19. 369._n 1^p+2^p+3^p++n^pn^p+1 is:
  20. 370.[ ( x - 1 ) 1 + ( x )^2 ^2,,dx ] is equal to
  21. 371.The value of [ 2 xdx ( x - 4 ) ] is
  22. 372.The integral [ ( 1 + x - 1 x )e^x + 1 xdx ] is equal to
  23. 373.The integral [ 2x^12 + 5x^9 ( x^5 + x^3 + 1 )^3 dx] is equal to :
  24. 374.If [ dx ^3x 2 2x = ( x )^A + C( x )^B + k,] where k is a constant of integration, then A +…
  25. 375.Let [I_n = ^nx,dx ,,( n > 1 ).] If I_4 + I_6 = [a ^5x + bx^5 + C], where C is a constant o…
  26. 376.The integral [ 1 + 2 x( ecx + x), ,,dx ] [( 0 < x < 2 )] is equal to : (where C is a const…
  27. 377.The integral [ ^2x ^2x ( ^5x + ^3x ^2x + ^3x ^2x + ^5x )^2 dx] is equal to
  28. 378.If [ x 1 + x + ^2xdx = x - K A ^ - 1 ] [( K, x + 1 A ) + C,(C,,] is a constant of integrat…
  29. 379.If [ x^5 e^ - x^2dx = g( x )e^ - x^2 + c], where c is a constant of integration, then [g(-…
  30. 380.If [ , ]x5.e-4x3 dx = [1 48]e-4x3 f(x) + C, where C is a constant of inegration, then f(x)…
  31. 381.Let n [ ] 2 be a natural number and [0 < < 2.] Then [ ( ^n - )^1/n ^n + 1 ,d ] is equal to…
  32. 382.The integral [ 2x^3 - 1 x^4 + x dx] is equal to : (Here C is a constant of integration)
  33. 383.The integral [ 3x^13 + 2x^11 ( 2x^4 + 3x^2 + 1 )^4 ,dx] is equal to : (where C is a consta…
  34. 384.The integral [ , ]cos(loge x) dx is equal to : (where C is a constant of integration)
  35. 385.[ e^ x] [( x xf(x) + x x + sex^2x)dx] = esecxf(x) + C then a possible choice of f(x) is :-
  36. 386.The integral [ sec^2/ 3,x ,cosec^4 / 3x ,dx ] is equal to (Hence C is a constant of integr…
  37. 387.If [f( x ) = 5x^8 + 7x^6 ( x^2 + 1 + 2x^7 )^2 ,dx,,( x 0 ),] [f( 0 ) = 0,] then the value …
  38. 388.For x2 [ ] n[ ] + 1, n [ ] N (the set of natural numbers), the integral [ x 2 (x^2 - 1) - …
  39. 389.The integral [ ( x x x + x )^2dx ] is equal to (where C is a constant of integration):
  40. 390.Let [f( x ) = x ( 1 + x )^2dx( x 0 ) ].
  41. 391.If [ ( e^2x + 2e^x - e^ - x - 1 )e^( e^x + e^ - x )dx ] = [g( x )e^( e^x + e^ - x ) + c] w…
  42. 392.If [ xdx ^3x( 1 + ^6x )^2/3 = f( x )( 1 + ^6x )^1/ + c] where c is a constant of integrati…
  43. 393.If f'(x) = tan--1(secx + tanx), [ - 2 < x < 2], and f(0) = 0, then f(1) is equal to :
  44. 394.The integral [ (2x - 1) (2x - 1)^2 + 5 4x^2 - 4x + 6 dx] is equal to (where c is a constan…
  45. 395.The integral [ e^3 _e2x + 5e^2 _e2x e^4 _ex + 5e^3 _ex - 7e^2 _ex dx], x > 0, is equal to …
  46. 396.The value of the integral [ . 2 ( ^6 + ^4 + ^2 ) 2 ^4 + 3 ^2 + 6 1 - 2 ,d ] is :
  47. 397.The integral [ 1 4 (x - 1)^3(x + 2)^5 ,dx] is equal to : (where C is a constant of integra…
  48. 398.[ The integral (1-1√3)( x- x)(1+2√3 2 x) d x is equal to ]
  49. 399.If [ 1 x 1 - x 1 + x dx = g(x) + c ], g(1) = 0, then [g( 1 2 )] is equal to :
  50. 400.If [ (x^2 + 1)e^x (x + 1)^2dx = f(x)e^x + C ], where C is a constant, then [d^3f dx^3] at …