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Integrate the following. (i) 1/(16 - x...

Integrate the following.
(i) `1/(16 - x^2) " " (ii) 1/(7 - (4x + 1)^2) " " (iii) 1/(5 - 6x - 9x^2)`

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The correct Answer is:
`(i) 1/8 log (4 - x)/(4 - x) + c`
(ii) `1/(8sqrt7) log ((sqrt(7) + (4x + 1))/(sqrt(7) - (4x + 1))) + c`.
(iii) `1/(6sqrt(6)) log ((sqrt(6) - (3x + 1))/(sqrt(6) - (3x + 1))) + c`.
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FULL MARKS-INTEGRAL CALCULUS-ADDITIONAL PROBLEMS
  1. Integrate: int x^2 e^(2x) dx

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  2. Integrate with respect to x (sin^(-1)x) (e^(sin^(-1)x))/(sqrt(1 - x...

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  3. Integrate: int "cosec"^(3)x dx.

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  4. Integrate: int sec^2 2x dx

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  5. Integrate the following with respect to x. e^(2x) sin 3x dx.

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  6. Integrate the following with respect to x. e^x cos 2x

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  7. Integrate the following with respect to x. e^(3x) sin 2x.

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  8. Integrate the following. (i) 1/(16 - x^2) " " (ii) 1/(7 - (4x + ...

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  9. Integrate the following with respect to x. (i) 1/((2x + 1)^2 - 16) "...

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  10. Integrate the following with respect to x. 1/(sqrt(x^2 + 8x - 20))

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  11. Integrate the following with respect to 'x' : (2x - 1)/(2x^2 + x + 3...

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  12. Integrate the following with respect to 'x' : (4x + 1)/(x^2 + 3x + 1...

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  13. Integrate the following with respect to 'x' : (2x - 3)/(sqrt(10 - 7...

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  14. (6x + 7)/(sqrt((x -4)(x - 5)))

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  15. Integrate the following functions with respect to x. sqrt((x + 1)^2...

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  16. Integrate the following functions with respect to x. sqrt((2x + 1)^2...

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  17. Integrate the following functions with respect to x. sqrt(x^2 - 3x +...

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  18. Integrate the following functions with respect to x. sqrt(169 - (3x ...

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  19. Integrate the following functions with respect to x. sqrt(1 - 3x - x...

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  20. Integrate the following functions with respect to x. sqrt((2 - x)(3 ...

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