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Evaluate the following integrals: int (d...

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

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The correct Answer is:
`1/2log|x+1|-1/4log(x^(2)+1)+1/2tan^(-1)x+C`
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BETTER CHOICE PUBLICATION-INTEGRALS-ASSIGNMENT (SECTION VIII MOST IMPORTANT QUESTIONS FOR PRACTICE)
  1. Evaluate the following integrals: int (x^(2)+1)/(x^(2)-5x+6)dx

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

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

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  4. Evaluate the following integrals: int (sinx)/((1-cosx)(2-cosx))dx

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  5. Evaluate the following integrals: int (sin2x)/((1+sinx)(2-sinx))dx

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  6. Evaluate the following integrals: int 1/(sinx-sin2x)dx

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

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  8. Evaluate the following integrals: int (x^(2)+1)/((x^(2)+4)(x^(2)+25))d...

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  9. Evaluate the following integrals: int 1/(x(x^(4)+1))dx

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  10. Evaluate the following integrals: int 1/(x(x^(3)+8))dx

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  11. Evaluate the following integrals: int 1/(x(x^(7)-1))dx

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  12. Evaluate the following integrals: int 1/(e^(x)-1)dx

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

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

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

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  16. Evaluate the following integrals: int (3x+5)/(x^(3)-x^(2)-x+1)dx

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  17. Evaluate the following integrals: int (5x)/((x+1)(x^(2)+9))dx

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  18. Evaluate the following integrals: int 5/((x+2)(x^(2)+1))dx

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

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

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