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If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^...

If `int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c`, then (a) `f(x)` is an even function (b) `f(x)` is a bounded function (c) the range of `f(x)` is `(0,1)` (d) `f(x)` has two points of extrema

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. int (dx)/((x+1)(x-2))=A log (x+1)+B log (x-2)+C, where

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  2. Each question has four choices, a,b,c and d, out of which only one i...

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

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

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

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

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

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  9. int(4e^x+6e^(-x))/(9e^x-4e^(-x))dx=A x+Blog(9e^(2x)-4)+C ,t h e n A= ...

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  10. The value of the integral int(cos^3x+cos^5x)/(sin^2x+sin^4x)dxi s si...

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  11. Evaluate: intsin^(-1)((2x+2)/(sqrt(4x^2+8x+13)))dx

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  12. Evaluate: for m in N , intx^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx...

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

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  14. Evaluate: int sqrt(1+cosec x) dx ,(0 < x < pi/2)

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

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

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  17. Evaluate: int(dx)/(x^3sqrt(x^2-1))

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

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  19. Evaluate: intsqrt(secx-1)dx

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  20. Evaluate: intsqrt((3-x)/(3+x))sin^(-1)(1/6sqrt(3-x))dx

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