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Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3t...

`Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n`
a) both `f(x)a n dg(x)` are odd functions
`b) f(x)` is monotonic function
`c) f(x)=g(x)` has no real roots
`d) int(f(x))/(g(x))dx=-1/x+3/(x^3)+c`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Each question has four choices, a,b,c and d, out of which only one i...

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  2. If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c, then (a) f(x) is an ...

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  3. Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n a) bo...

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  4. If intsin^(-1)xcos^(-1)xdx=f^(-1)(x)[π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+...

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  5. If int(cos4x+1)/(cotx-tanx)dx = Acos4x+B ,t h e n (a)A=-1/8 (b) B=1/...

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  6. Statement 1: int(dx)/(x^3sqrt(1+x^4))=-1/2sqrt(1+1/(x^4))+C Statement...

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  7. Statement 1: int(sinxdx)/x ,(x >0), cannot be evaluated. Statement 2...

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  8. If int (4e^x + 6e^-x)/(9e^x - 4e^-x) dx = Ax + B loge(9e^(2x) - 4) + c...

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  9. int (cos^3 x + cos^5 x)/(sin^2 x + sin^4 x) dx equals

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  10. If int sin^-1 ((2x + 2)/sqrt(4x^2 + 8x + 13)) dx = (x + 1) tan^-1 ((2x...

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  11. Evaluate for m in N , int(x^(3m)+x^(2m)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx...

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  12. Evaluate: int(cos^4x)/(sin^3x(sin^5x+cos^5x)^(3/5))dx

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  13. Evaluate: int sqrt(1+cosecx dx)

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

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  15. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

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  16. Evaluate: int(x^3)/(sqrt(x^2+1))dx

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  17. Evaluate : int(2x)/((1-x^2)sqrt(x^4-1))dx

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  18. Evaluateintsqrt(secx-1)dx, 0ltxltpi/2

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  19. Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))

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  20. Evaluate: If intcos^nxdotdx prove that In=1/n(cos^(n-1)xsinx)+((n-1)/n...

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