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intfrac{5x-1}{3x^2+x+2}dx =....(5/6)log|...

`intfrac{5x-1}{3x^2+x+2}dx` =....`(5/6)log|3x^2+x+2|+frac{11}{3sqrt 23}tan^(-1)(frac{6x+1}{sqrt 23})+c` `(5/6)log|3x^2+x+2|-frac{11}{3sqrt 23}tan^(-1)(frac{6x+1}{sqrt 23})+c` `(-5/6)log|3x^2+x+2|+frac{11}{3sqrt 23}tan^(-1)(frac{6x+1}{sqrt 23})+c` `(-5/6)log|3x^2+x+2|-frac{11}{3sqrt 23}tan^(-1)(frac{6x+1}{sqrt 23})+c`

A

(5/6) log|3`x^2` + x + 2| + `frac{11}{3`sqrt 23}` `tan^(-1)` (`frac{6x+1}{`sqrt 23`}` )+ c

B

(5/6) log|3`x^2` + x + 2| - `frac{11}{3`sqrt 23}` `tan^(-1)` (`frac{6x+1}{`sqrt 23`}` )+ c

C

-(5/6) log|3`x^2` + x + 2| + `frac{11}{3`sqrt 23}` `tan^(-1)` (`frac{6x+1}{`sqrt 23`}` )+ c

D

(5/6) log|3`x^2` + x + 2| - `frac{11}{3`sqrt 23}` `tan^(-1)` (`frac{6x+1}{`sqrt 23`}` )+ c

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CHETANA PUBLICATION-Indefinite Integration-Exercise
  1. int frac{1}{x^2 + 4x + 8} dx =............... A) tan^(-1) (frac{x+2}{...

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  2. int frac{1}{sqrt (3 + 4x - 4 x^2)} dx =............... A) sin^(-1) fr...

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  3. intfrac{5x-1}{3x^2+x+2}dx =....(5/6)log|3x^2+x+2|+frac{11}{3sqrt 23}ta...

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  4. int frac {x+1}{x+2} dx =............ A) x+2 - log(x+2) + c B) sqrt (...

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  5. intfrac{1}{4+5sin x}dx=..............a)(1/3)log |frac{2tan(x/2)+4}{2ta...

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  6. int sqrt (frac{a+x}{a-x}) dx =................ A) -a cos^(-1) (x/a) -...

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  7. intx^2e^(3x) dx=............ A) (1/3) x^2e^(3x) - (2/9) x e^(3x) + (2...

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  8. int tan^(-1)sqrt x dx=.............a)xtan^(-1)sqrt x - sqrt x + tan^(-...

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  9. int e^x frac{x}{(x+1)^2} dx =........... A) e^x(x+1) + c B) frac{e^x...

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  10. intfrac{x+1}{x^2 + 5x + 6} dx=............ A) log(x+2) +2 log(x+3) +...

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  11. intfrac{ t^2 + 1}{ t^4 + 1} dt=...........a) frac{1}{sqrt2}[tan^(-1)(s...

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  12. intfrac{1}{4+5 cos^2 x} dx=.............. A) (1/3)tan^(-1)((2/3)tan x...

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  13. intsin^(-1) x dx=............ A) x sin^(-1) x + sqrt (1-x^2) + c B) ...

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  14. int frac{e^(1/x)}{x^2} dx=........... A) frac{e^(1/x)}{x^2} + c B) 1...

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  15. int frac{dx}{1+e^(-x)} =........... A) log(1+e^(-x)) + c B) log(e^x ...

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  16. int sin^2 x cos^2 x dx=............. A) 1/8(x-frac{sin 4x}{4}) + c B...

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  17. int frac{1}{ 3 x- 2 sqrt x} dx=..........

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  18. intfrac{x^2 + 3x +5}{(x+2)(x^2 + 2x +3)} dx=............ (A) log (x+2...

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  19. Evaluate the following: inttan^2 x dx

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  20. Evaluate the following: int x root(3)(x) dx

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