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Integrate the functions (sqrt(x^(2)+1)...

Integrate the functions
`(sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))`

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Verified by Experts

The correct Answer is:
`-1/3(1+1/(x^(2)))^(3/2)[log(1+1/(x^(2)))-2/3]+C`
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NCERT TAMIL-INTEGRALS-EXERCISE 7.12
  1. Integrate the functions (x^(2)+x+1)/((x+1)^(2)(x+2))

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  2. Integrate the functions tan^(-1)x

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  3. Integrate the functions (sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))

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  4. Evaluate the definite integrals int(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx...

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  5. Evaluate the definite integrals int(0)^(pi/4)(sinxcosx)/(cos^(4)x+si...

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  6. Evaluate the definite integrals int(0)^((pi)/(2))(cos^(2)xdx)/(cos^...

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  7. Evaluate the definite integrals int((pi)/(6))^((pi)/(3))(sinx+cosx)...

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  8. Evaluate the definite integrals int(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

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  9. Evaluate the definite integrals int(0)^((pi)/(4))(sinx+cosx)/(9+16s...

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  10. Evaluate the definite integrals int(0)^((pi)/(2))sin2xtan^(-1)(sinx...

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  11. Evaluate the definite integrals int(0)^(pi)(xtanx)/(secx+tanx)dx

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  12. Evaluate the definite integrals int(1)^(4)[abs(x-1)+abs(x-2)+abs(x-3...

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  13. Prove the following int(1)^(3)(dx)/(x^(2)(x+1))=(2)/(3)+"log"(2)/(3)

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  14. Prove the following int(0)^(1)xe^(x)dx=1

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  15. Prove the following int(-1)^(1)x^(17)cos^(4)xdx=0

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  16. Prove the following int(0)^(pi/2)sin^(3)xdx=2/3

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  17. Prove the following int(0)^(pi/4)2tan^(3)xdx=1-log2

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  18. Prove the following int(0)^(1)sin^(-1)xdx=(pi)/(2)-1

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  19. Evaluate int(0)^(1)e^(2-3x)dx as a limit of a sum.

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  20. int(dx)/(e^(x)+e^(-x)) is equal to

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