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For integral int f(x- a/x)*(1+a/x^(2))dx...

For integral `int f(x- a/x)*(1+a/x^(2))dx`, put `x-a/x=t`
For integral `int f(x+a/x)*(1-(a)/(x^(2)))dx`, put `x+a/x =t`
For integral `int f(x^(2)-(a)/(x^(2)))*(x+(a)/(x^(3)))dx`, put `x^(2)-(a)/(x^(2))=t`
For integral `int f(x^(2)+(a)/(x^(2)))*(x-(a)/(x^(3)))dx`, put `x^(2)+(a)/(x^(2))=t`
many integrands can be brought into above forms by suitable reductions or transformations .
`int(x^(4)-2)/(x^(2)sqrt(x^(4)+x^(2)+2))dx`

A

`sqrt(x^(2)+1+(1)/(x^(2)))+C`

B

`sqrt(x^(2)+1+(2)/(x^(2)))+C`

C

`sqrt(x^(2)+(1)/(x^(2)))+C`

D

`sqrt(x^(2)+(2)/(x^(2)))+C`

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For integral int f(x- a/x)*(1+a/x^(2))dx , put x-a/x=t For integral int f(x+a/x)*(1-(a)/(x^(2)))dx , put x+a/x =t For integral int f(x^(2)-(a)/(x^(2)))*(x+(a)/(x^(3)))dx , put x^(2)-(a)/(x^(2))=t For integral int f(x^(2)+(a)/(x^(2)))*(x-(a)/(x^(3)))dx , put x^(2)+(a)/(x^(2))=t many integrands can be brought into above forms by suitable reductions or transformations . int(5x^(4)+4x^(5))/((x^(5)+x+1)^(2))dx

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FIITJEE-INDEFINTE INTEGRAL-SOLVED PROBLEMS (OBJECTIVE)
  1. If int(cos^(2)x)/(sin^(6)x)dx=Acot^(5)x+Bcot^(3)x+k, then A+B equals

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  2. If f'(x)=x|sinx|AAx""in(0,x)andf(0)=(1)/(sqrt3), then f(x) will be

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  3. int((x^(2)-1))/((x^(2)+1)sqrt(x^(4)+1))dx is equal to

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  4. Evaluate: int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3))).dx

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  5. If int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx=mue^(x)((1+x)/(1-x))^(la...

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  6. int(dx)/(xsqrt(1-x^(3)))dx=

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  7. he value of the integral inte^(sin^(2x))(cosx+cos^3x)sinx dx is

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  8. If int(dx)/(5+4cosx)=ktan^(-1)(mtan""(x)/(2))+c, then

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  9. If intsqrt(cosecx+1)dx,kfog(x)+c, where k is a real constant, then

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  10. If f'(x)=(1)/(-x+sqrt(x^(2)+1))andf(0)=(-(1+sqrt2))/(2), then the valu...

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  11. int(dx)/(root(3)((x-1)^(4)*(x+1)^(2)))

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  12. I=int (dx)/(""^(4)sqrt( (x-1) ^(3) (x+2)^(5)))=k ""^(4)sqrt((x-1)/(x+2...

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  13. For integral int f(x- a/x)*(1+a/x^(2))dx, put x-a/x=t For integral i...

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  14. Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x))\ dx

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  15. Statement -1 : Integral of an even function is not always on odd funct...

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  16. If int(lnx)/(x^(3))dx=-(lnx)/(ax^(2))-(1)/(bx^(2))+c then the value of...

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  17. Evaluate : intsin4x.e^(tan^(2)x)dx

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  18. If the primitive of the function f(x)=(x^(2009))/((1+x^(2))^(1006)) w....

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  19. If the antiderivative of (x^(3))/(sqrt((1+2x^(2)))) which passes throu...

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  20. Match the following:

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