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Evaluate the following integrals: intt...

Evaluate the following integrals:
`inttan^(-1)((3x-x^(3))/(1-3x^(2)))dx`

Text Solution

Verified by Experts

The correct Answer is:
`3xtan^(-1)x-(3)/(2)log(1+x^(2))+C`
Put `x=tant anddx=sec^(2)"t dt. Use "((3tant-tan^(3)t)/(1-3tan^(2)t))=tan3t`.
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RS AGGARWAL-METHODS OF INTEGRATION -Exercise 13C
  1. Evaluate the following integrals: intcos^(-1)((1-x^(2))/(1+x^(2)))dx

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

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

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

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

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

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

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

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

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  10. Evaluate the following integrals: inte^(-x)cosxdx

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  11. Evaluate the following integrals: inte^(x)(sinx+cosx)dx

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  12. Evaluate the following integrals: inte^(x)(cotx-"cosec"^(2)x)dx

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  13. Evaluate the following integrals: inte^(x)secx(1+tanx)dx

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  14. Evaluate the following integrals: inte^(x)(tan^(-1)x+(1)/(1+x^(2)))d...

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  15. inte^(x)(cotx+logsinx)dx=?

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  16. inte^x(tanx-logcosx)dx

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  17. inte^(x)[secx+log(secx+tanx)]dx=?

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  18. Evaluate the following integrals: inte^(x)((1+sinxcosx)/(cos^(2)x))d...

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  19. Evaluate the following integrals: inte^(x)((sinxcos-1)/(sin^(2x)))dx

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  20. Evaluate the following integrals: inte^(x)((cosx+sinx)/(cos^(2)x))dx

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