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Evaluate the following integrals: int (...

Evaluate the following integrals:
`int (x^(2)+x+1)/((x+2)(x^(2)+1))dx`

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The correct Answer is:
`3/4log|x+2|+1/5log(x^(2)+1)+1/5tan^(-1)x+C`
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BETTER CHOICE PUBLICATION-INTEGRALS-PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Evaluate the following integrals: int (dx)/(x^(2)-6x+13)

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  2. Evaluate the following integrals: int 1/(3x^(2)+13x-10)dx

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  3. Evaluate the following integrals: int (x^(2)+x+1)/((x+2)(x^(2)+1))dx

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  4. Find: int ((3sinphi-2)cosphi)/(5-cos^2phi-4sinphi)dphi

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  5. Evaluate the following integrals: int(0)^(pi//2)(sinx-cosx)/(1+sinx c...

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  6. Evaluate the following integrals: int(-pi//4)^(pi//4)sin^(2)x dx

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  7. Evaluate the following integrals: int(-pi//4)^(pi//2)sin^(2)x dx

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  8. Prove that: int(0)^(2pi)cos^(5)x=0

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  9. Evaluate int(0)^(pi)log(1+cosx)dx

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  10. Evaluate the following integrals : int1/(sqrt(x)-x)dx

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  11. Evaluate the following integrals : int 1/ (x-sqrt(x))dx

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  12. Evaluate the following integrals : int 1/(cos^(2)x+2sin^(2)x)dx

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  13. Evaluate the following integrals : int 1/(sin^(2)x+4cos^(2)x)dx

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  14. Evaluate int0^(pi/2) (cosx)/((2+sinx)(3+sinx) ) dx

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  15. Evaluate int0^(pi/2) (cosx)/((3+sinx)(4+sinx) ) dx

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  16. Evaluate the following integrals : int(0)^(pi//2)(cosx)/((4+sinx)(5+...

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  17. Evaluate the following integrals : int(0)^(pi//2)(2sinx+3cosx)/(sinx...

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  18. Using properties of definite integrals, show that int(0)^(pi//2)(xdx...

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  19. Using properties of definite integrals, show that int(0)^(pi//2)(sin...

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  20. Prove that : int0^pi (xtanx)/(secxcosecx)dx =pi^2/4.

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