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Evaluate the following integrals: int(...

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

Text Solution

Verified by Experts

The correct Answer is:
`(-1)/((x+2))-(log(x+2))/((x+2))+C`
Integrate by parts, taking log (x+2) as the 1st function and `(1)/((x+2)^(2))` as the 2nd function.
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RS AGGARWAL-METHODS OF INTEGRATION -Exercise 13C
  1. Evaluate the following integrals: int(xsin^(-1)x)/(sqrt(1-x^(2)))dx

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

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

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  4. Evaluate the following integrals: intxsin^(-1)xdx

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  5. Evaluate the following integrals: intxcos^(-1)xdx

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  6. Evaluate the following integrals: intcot^(-1)xdx

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  7. Evaluate the following integrals: intxcot^(-1)xdx

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  8. Evaluate the following integrals: intx^(2)cot^(-1)xdx

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  9. Evaluate the following integrals: intsin^(-1)sqrt(x)dx

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  10. Evaluate the following integrals: intcos^(-1)sqrt(x)dx

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  11. Evaluate the following integrals: intcos^(-1)(4x^(3)-3x)dx

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

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  13. Evaluate the following integrals: inttan^(-1)((2x)/(1-x^(2)))dx

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  14. Evaluate the following integrals: inttan^(-1)((3x-x^(3))/(1-3x^(2)))...

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

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  16. Evaluate the following integrals: int(tanxsec^(2)x)/((1-tan^(2)x))dx

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  17. Evaluate the following integrals: inte^(3x)sin4xdx

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  18. Evaluate the following integrals: inte^(2x)sinxdx

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  19. Evaluate the following integrals: inte^(2x)sinxcosxdx

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  20. Evaluate the following integrals: inte^(2x)cos(3x+4)dx

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