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Integrate the functions 1/(x^(1/2)+x^(...

Integrate the functions
`1/(x^(1/2)+x^(1/3))` [Hint: `1/(x^(1/2)+x^(1/3))=1/(x^(1/3)(1+x^(1/6)))`, put `x=t^(6)`]

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Verified by Experts

The correct Answer is:
`2 sqrt(x)-3x^((1)/(3))+6x^((1)/(6))-6log|x^((1)/(6))+1|+c`
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KUMAR PRAKASHAN-INTEGRALS -MISCELLANEOUS EXERCISE-7
  1. Integrate the functions 1/(xsqrt(ax-x^(2))) [Hint: Put x =a/t]

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  2. Integrate the function is Exercise. (I)/(x^(2)(x^(4)+1)^((3)/(4)))

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  3. Integrate the functions 1/(x^(1/2)+x^(1/3)) [Hint: 1/(x^(1/2)+x^(1/3...

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  4. Integrate the functions (5x)/((x+1)(x^(2)+9))

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  5. Integrate the functions (sinx)/(sin(x-a))

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  6. Integrate the function is Exercise. (e^(5 log)-e^(4logx))/(e^(3logx)...

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  7. Integrate the function (x+2)/(sqrt(4x-x^(2)))

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  8. Integrate the functions (sin^(8)-cos^(8)x)/(1-2sin^(2)xcos^(2)x)

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  9. Find the integrals of the functions 1/(cos(x – a) cos (x – b))

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  10. Integrate the functions (x^(3))/(sqrt(1-x^(8)))

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  11. Integrate the functions (e^(x))/((1+e^(x))(2+e^(x)))

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  12. Integrate the function is Exercise. (1)/((x^(2)+1)(x^(2)+4))

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  13. Integrate the function is Exercise. cos^(3)x e^(log sinx)

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  14. Integrate the functions e^(3logx)(x^(4)+1)^(-1)

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  15. Integrate the functions f'(ax+b)[f(ax+b)]^(n)

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  16. Integrate the function is. (1)/(sqrt(sin^(3)x sin(x+alpha)))

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  17. Integrate the function is Exercise. (sin^(-1) sqrt(x)-cos^(-1)sqrt(x...

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  18. Integrate the function is Exercise. sqrt((1-sqrt(x))/(1+sqrt(x)))

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  19. Integrate the functions (2+sin2x)/(1+cos2x)e^(x)

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  20. Integrate the function is Exercise. (x^(2)+x+1)/((x+1)^(2)+(x+2))

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