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intfrac{ t^2 + 1}{ t^4 + 1} dt=............

`int``frac{ t^2 + 1}{ t^4 + 1}` dt=...........a) `frac{1}{sqrt2}[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c` b) `sqrt2[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c` c)` frac{1}{2sqrt2}[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c` d) `2sqrt2[tan^(-1)(sqrt 2t-1)+tan^(-1)(sqrt 2t+1)]+c`

A

`frac{1}{`sqrt 2`} `tan^(-1)`(`frac{`t^2` -1}{`sqrt 2`}`) + c

B

`frac{1}{2`sqrt 2`} `tan^(-1)`(`frac{`t^2` -1}{`sqrt 2`}`) + c

C

`frac{1}{`sqrt 2`} `tan^(-1)`(`frac{`t^2` -1}{`sqrt (2t)`}`) + c

D

`frac{1}{2`sqrt 2`} `tan^(-1)`(`frac{`t^2` -1}{`sqrt (2t)`}`) + c

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CHETANA PUBLICATION-Indefinite Integration-Exercise
  1. int e^x frac{x}{(x+1)^2} dx =........... A) e^x(x+1) + c B) frac{e^x...

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

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

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

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

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

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

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

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

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

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  11. Evaluate the following: inttan^2 x dx

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

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  13. Evaluate: int log x dx

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  14. Evaluate: int e^x (sin x+ cos x) dx

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  15. Evaluate: int frac{1}{x^2 + 2x + 5} dx

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  16. Evaluate: int frac{x}{x^27} dx

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  17. Prove that int frac{1}{sqrt (x^2 - a^2)} dx = log (x+ sqrt (x^2 -a^2))...

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  18. Evaluate int frac{x+3}{sqrt (x^2 + 2x + 2)} dx

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  19. Evaluate int frac{x^2}{(x^2 + 4)(x^2 + 9)} dx

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  20. Evaluate the following: int x tan^(-1) x dx

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