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Evaluate the following integrals : int...

Evaluate the following integrals :
`int((x^(4)-x)^(1//4))/(x^(5))dx`.

Text Solution

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The correct Answer is:
`t=1-(1)/(x^(3))`
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ARIHANT PUBLICATION-INTEGRATION -PART II (QUESTION FOR PRACTICE) (4 MARK)
  1. Evaluate the following integrals : int((x^(4)-x)^(1//4))/(x^(5))dx.

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

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  3. Evaluate the following integrals : intsqrt((1+x)/(1-x))dx,x!=1.

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

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  5. Evaluate the following integrals : int(dx)/(x^(1/2)+x^(1/3))

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  6. Evaluate the following integrals : int sin x sin 2x sin 3xdx.

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  7. Evaluate the following integrals : intsin^(4)x cos^(3)x dx.

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  8. Evaluate the following integrals : int(cosx-cos2x)/(1-cosx)dx

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  9. Integrate : int (sin6x + sin4x) / (cos6x + cos4x) dx.

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  10. Evaluate the following integrals : inttan^(-1)sqrt((1-cosx)/(1+cosx))...

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  11. Evaluate the following integrals : int(sin^(6)x+cos^(6)x)/(sin^(2)x*c...

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  12. Evaluate the following integrals : int(cos^3x)/(1+cos2x)dx.

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  13. Evaluate the following integrals : int(dx)/(x[(logx)^(2)+25])

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  14. Evaluate the following integrals : int(x+3)/(x^(2)-2x-5)dx.

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

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  16. Evaluate the following integrals : int(6x+7)/(sqrt(3x^2+7x))dx.

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

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  18. Evaluate the following integrals : int(sinx)/(sin3x)dx.

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  19. Evaluate the following integrals : int(dx)/(2sin^(2)x+5cos^(2)x)dx.

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

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