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int frac{e^(2x) + e^(-2x)}{e^x} dx =.......

`int` `frac{e^(2x) + e^(-2x)}{e^x}` dx =............. A) `e^x - frac{1}{3 e^(3x)}` + c B) `e^x + frac{1}{3 e^(3x)}` + c C) `e^(-x) + frac{1}{3 e^(3x)}` + c D) `e^(-x) - frac{1}{3 e^(3x)}` + c

A

`e^x - frac{1}{3 e^(3x)}` + c

B

`e^x + frac{1}{3 e^(3x)}` + c

C

`e^(-x) + frac{1}{3 e^(3x)}` + c

D

`e^(-x) - frac{1}{3 e^(3x)}` + c

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int frac{e^(1/x)}{x^2} dx=........... A) frac{e^(1/x)}{x^2} + c B) 1/4 e^(1/x) + c C) -e^(1/x) + c D) e^(1/x) + c

int frac{e^x(1+x)}{ cos^2 (x e^x)} dx=.............. A) tan(x e^x ) + c B) - tan(x e^x ) + c C) cot(x e^x ) + c D) -cot(x e^x ) + c

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

int frac{log x}{(log ex)^2} dx= ............ A) frac{x}{1+log x} + c B) x(1+log x) + c C) frac{1}{1+log x} + c D) frac{1}{1-log x} + c

int frac{1}{sqrt (3 + 4x - 4 x^2)} dx =............... A) sin^(-1) frac{2x-1}{2} + c B) (1/2) sin^(-1) frac{2x-1}{2} + c C) (1/3) sin^(-1) frac{2x-1}{2} + c D) (1/2) sin^(-1) (2x-1) + c

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int x^2 e^(3x) dx=............ A) (1/3) x^2 e^(3x) - (2/9) x e^(3x) + (2/27) e^(3x) + c B) -(1/3) x^2 e^(3x) - (2/9) x e^(3x) + (2/27) e^(3x) + c C) (1/3) x^2 e^(3x) + (2/9) x e^(3x) - (2/27) e^(3x) + c D) (1/3) x^2 e^(3x) - (2/9) x e^(3x) - (2/27) e^(3x) + c

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

CHETANA PUBLICATION-Indefinite Integration-Exercise
  1. int [ sin(log x) + cos(log x)] dx=........... A) x cos(log x) + c B) ...

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  2. intfrac{cos 2x -1}{cos 2x + 1} dx=........... A) tan x - x + c B) x ...

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  3. int frac{e^(2x) + e^(-2x)}{e^x} dx =............. A) e^x - frac{1}{3 ...

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  4. int frac{sin^4 2x + cos^4 2x}{sin^2 2x cos^2 2x} dx=.............

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  5. int e^(3 log x) (x^4 + 1)^(-1) dx =............. A) (1/2) tan^(-1) (x...

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  6. int frac{e^x(1+x)}{ cos^2 (x e^x)} dx=.............. A) tan(xe^x) + c...

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  7. int frac{1}{sin(x-a) sin(x-b)} dx =.......... A) int frac{1}{sin(b-a)...

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  8. int frac{1}{x^2 + 4x + 8} dx =............... A) tan^(-1) (frac{x+2}{...

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

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

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

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

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

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

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

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

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

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

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

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

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