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Evaluate the following integrals: int(...

Evaluate the following integrals:
`int(cos^(9)x)/(sinx)dx`

Text Solution

Verified by Experts

The correct Answer is:
`log|sinx|-2sin^(2)x+(3)/(2)sin^(4)x-(2)/(3)sin^(6)x+(1)/(8)sin^(8)x+C`
`I=int(cos^(8)xcosx)/(sinx)dx=int((1-sin^(2)x)cosx)/(sinx)dx`. Put sin x=t.
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RS AGGARWAL-METHODS OF INTEGRATION -Exercise 13B
  1. Evaluate the following integrals: intsin^(3)xcosxdx

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  2. Evaluate the following integrals: intsec^(4)dx

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  3. Evaluate the following integrals: intcos^3xsin^(4)dx

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  4. Evaluate the following integrals: intcos^(4)xsin^(3)xdx

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  5. Evaluate the following integrals: intsin^(2//3)xcos^(3)xdx

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  6. Evaluate the following integrals: intcos^(3//5)xsin^(3)xdx

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  7. Evaluate: intcos e c^4\ 2x\ dx

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  8. Evaluate the following integrals: int(cos2x)/(cosx)dx

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  9. Evaluate the following integrals: int(cosx)/(cos(x+alpha))dx

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  10. Evaluate the following integrals: intcos^(3)xsin2xdx

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  11. Evaluate the following integrals: int(cos^(9)x)/(sinx)dx

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  12. Evaluate the following integrals: intcos^(4)2xdx

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

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  14. Evaluate the following integrals: int(dx)/((3cosx+4sinx))

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  15. Evaluate the following integrals: int(dx)/((acosx+bsinx)^(2)),agt0an...

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  16. Evaluate the following integrals: int(dx)/((cosx-sinx))

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  17. Evaluate the following integrals: int(2tanx-3cotx)^(2)dx

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  18. Evaluate the following integrals: intsinxsin2xsin3x

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  19. Evaluate the following integrals: int((1-cotx)/(1+cotx))dx

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  20. Evaluate the following integrals: int(dx)/((2sinx+cosx+3))

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