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inte^x(tanx-logcosx)dx...

`inte^x(tanx-logcosx)dx`

Text Solution

Verified by Experts

The correct Answer is:
`e^(x)log(secx)+C`
`I=inte^(x)(logsecx+tanx)dx=inte^(x){int(x)+f'(x)}dx," where "f(x)=logsecx`.
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RS AGGARWAL-METHODS OF INTEGRATION -Exercise 13C
  1. Evaluate the following integrals: inte^(x)(tan^(-1)x+(1)/(1+x^(2)))d...

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

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  3. inte^x(tanx-logcosx)dx

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

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

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

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

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  8. Evaluate the following integrals: inte^(x)((2-sin2x)/(1-cos2x))dx

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  9. inte^(x)((1+sinx)/(1+cosx))dx=?

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  10. Evaluate: inte^x\ ((sin4x-4)/(1-cos4x))\ dx

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  11. Evaluate the following integrals: int(e^(x)[sqrt(1-x^(2))sin^(-1)x+1...

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  12. Evaluate the following integrals: inte^(x)((1+xlogx)/(x))dx

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  13. Evaluate the following integrals: inte^(x)*(x)/((1+x)^(2))dx

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

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

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  16. Evaluate the following integrals: inte^(x)*((x-3))/((x-1)^(3))dx

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  17. Evaluate the following integrals: inte^(3x)((3x-1)/(9x^(2)))dx

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

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  19. int(x e^(2x))/((1+2x)^2)dx

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

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