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Evaluate the following integrals: (i) ...

Evaluate the following integrals:
(i) `int_(2)^(3)x^(2)dx` (ii) `int_(4)^(9)(sqrtx)/((30-x^(3/2))^(2))dx`
(iii) `int_(1)^(2)(xdx)/((x+1)(x+2))` (iv) `int_(0)^(pi/4)sin^(3)2tcos2tdt`

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NCERT GUJARATI-INTEGRALS-EXERCISE 7.12
  1. Evaluate the following integrals: (i) int(2)^(3)x^(2)dx (ii) int(4)^...

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  2. Integrate the functions 1/(x-x^(3))

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  3. Integrate the functions 1/(sqrt(x+a)+sqrt(x+b))

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  4. Integrate the functions 1/(xsqrt(ax-x^(2))) [Hint: Put x =a/t]

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  5. Integrate the functions 1/(x^(2)(x^(4)+1)^(3/4))

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

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

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

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  9. Integrate the functions (e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))

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  10. Integrate the functions (cosx)/(sqrt(4-sin^(2)x))

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

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  12. Integrate the functions 1/(cos(x+a)cos(x+b))

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

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

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

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  16. Integrate the functions cos^(3)xe^(logsinx)

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

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

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  19. Integrate the functions 1/(sqrt(sin^(3)xsin(x+alpha))

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  20. Integrate the functions (sin^(-1)sqrtx-cos^(-1)sqrtx)/(sin^(-1)sqrtx...

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  21. Integrate the functions sqrt((1-sqrtx)/(1+sqrtx))

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