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Evaluate the following integrals: int(2s...

Evaluate the following integrals:
`int(2sin 2 theta- cos theta)/(6-cos^2 theta- 4 sin theta)d theta`

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Evaluate the following integrals: 1/(1+2cos theta)d theta

Prove the following identity : (sin theta)/(1-cos theta)= (1+cos theta)/(sin theta) .

Prove the following identity : sin^6 theta+ cos^6 theta= 1-3 sin^2 theta cos^2 theta .

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

Find sin 2 theta when sin theta + cos theta= 1 .

Prove the following identity : (sin theta+ cos theta) (sec theta+ cosec theta) =2+ sec theta cosec theta .

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

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MODERN PUBLICATION-INTEGRALS-EXERCISE
  1. Evaluate the following integrals: int(logx)/(x(1+logx)(2+logx))dx

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  2. Evaluate the following integrals: int(1)/(x[6(logx)^2+7logx+2])dx

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  3. Evaluate the following integrals: int(2sin 2 theta- cos theta)/(6-cos^...

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

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

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  6. Evaluate the following integrals: int(x^4)/(x^4-16)dx

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  7. Evaluate the following integrals: int(dx)/(sqrt(x(1-2x)))

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

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  9. Evaluate the following integrals: int(dx)/(sqrt(5+4x-x^2))

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  10. Evaluate the following integrals: int(dx)/(sqrt(8+3x-x^2))

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  11. Evaluate the following integrals: int(dx)/(sqrt(16-6x-x^2))

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  12. Evaluate the following integrals: int(dx)/(sqrt(7-6x-x^2))

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

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  14. Evaluate the following integrals: int(1)/(sqrt(8+3x-x^2))dx

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  15. Evaluate the following integrals: int (dx)/(sqrt(2+7x-3x^(2)))

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

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  17. Evaluate the following integrals: int(dx)/(sqrt(x^2+6x+4))

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  18. Evaluate the following integrals: int (dx)/(sqrt((x-1)(x-2)))

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  19. Evaluate the following integrals: int(dx)/(sqrt((x-a)(x-b)))

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  20. Evaluate the following integrals: int (dx)/(sqrt(x)sqrt(5-x))

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