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Indefinite Integrals

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  1. 401.For [I(x)= ^2 x-2022 ^2022 x d x], if [I(()/(4))=2^1011], then
  2. 402.For [, , , N], if [(((x)/(e))^2 x+((e)/(x))^2 x) _e x d x=(1)/()((x)/(e))^ x-(1)/()((e)/(x…
  3. 403.Let [f(x) = 2x (x^2 + 1)(x^2 + 3)dx ].
  4. 404.Let [I(x)= x^2(x ^2 x+ x)(x x+1)^2 d x].
  5. 405.The integral [ [((x)/(2))^x+((2)/(x))^x] ((e x)/(2)) d x ] is equal to :
  6. 406.Let [I(x)= (x+1)x(1+x e^x)^2 d x, x > 0].
  7. 407.[ The integral (x^8-x^2) d x(x^12+3 x^6+1) ^-1(x^3+(1)/(x^3)) is equal to : ]
  8. 408.If [ ^(3)/(2) x+ ^(3)/(2) x ^3 x ^3 x (x-) d x=A x- +B - x+C], where C is the integration …
  9. 409.For [x (-()/(2), ()/(2))], if [y(x)= cosec x+ xcosec x x+ x ^2 x d x], and [ _x (()/(2))^-…
  10. 410.If [ 1a^2 ^2 x+b^2 ^2 x ~d x=(1)/(12) ^-1(3 x)+] constant, then the maximum value of [a x+…
  11. 411.Let [I(x)= (6)/( ^2 x(1- x)^2) d x].
  12. 412.Let [ (2- x)/(3+ x) ~d x=(1)/(2)( x+ _e| x+ x|)+C], where C is the constant of integration…
  13. 413.If e^x(x ^-1 x√1-x^2+ ^-1 x(1-x^2)^3 / 2+(x)/(1-x^2)) d x=g(x)+C, where C is the constant …
  14. 414.Let x^3 x ~d x=g(x)+C, where C is the constant of integration.
  15. 415.If f(x)= 1x^1 / 4(1+x^1 / 4) d x, f(0)=-6, then f(1) is equal to :
  16. 416.[ Let f(x)= x^3 √3-x^2 d x .