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int frac{x-sin x}{1-cos x} dx=.............

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

A

x cot(x/2) + c

B

- x cot(x/2) + c

C

cot(x/2) + c

D

x tan(x/2) + c

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int frac{1}{cos x - cos^2 x} dx=............ (A) log(cosec x - cot x) + tan(x/2) + c (B) sin 2x -cos x +c (C) log(sec x + tan x) - cot(x/2) + c (D) cos 2x - sin x + c

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

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

int frac{1}{x+x^5} dx = f(x) +c , then int frac{x^4}{x+x^5} dx = ............. A) log x -f(x) +c B) f(x) + log x +c C) f(x)-log x +c D) (1/5) x^5 f(x) +c

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CHETANA PUBLICATION-Indefinite Integration-Exercise
  1. int frac{sin^mx}{cos^(m+2)x} dx=.............. A) frac{tan^(m+1)x}{m+...

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  2. int tan(sin^(-1) x) dx=........... A) (1-x^2)^(1/2) + c B) -(1-x^2)^...

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  3. int frac{x-sin x}{1-cos x} dx=........... A) x cot(x/2) + c B) -x co...

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  4. If f(x) = frac{sin^(-1)x}{sqrt (1-x^2)}, g(x)=e^(sin^(-1)x), then int ...

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  5. If int tan^3 x sec^3 x dx=(1/m) sec^m x - (1/n) sec^n x dx , then (...

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  6. intfrac{1}{cos x - cos^2 x} dx=............ (A) log(cosec x - cot x) ...

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  7. int frac{sqrt (cot x)}{sin x cos x} dx =............ A) 2sqrt cot x +...

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

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  9. int sin(log x) dx=........ (A) (x/2)[sin(log x) - cos(log x)] + c (B)...

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  10. int x^x (1+ log x) dx =............. A) (1/2) (1+log x)^2 +c B) x^(x...

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  11. intcos^(-3/7)xsin^(-11/7)xdx=...... A) (-7/4)tan^(-4/7)x+c B) log(si...

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  12. 2 int frac{cos^2 x - sin^2 x}{cos^2 x + sin^2 x} dx=............ A) s...

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  13. int frac{1}{cos x sqrt (sin^2 x - cos^2 x)} dx=............ A) log(ta...

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  14. int frac{log x}{(log ex)^2} dx= ............ A) frac{x}{1+log x} + c ...

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  15. int [ sin(log x) + cos(log x)] dx=........... A) x cos(log x) + c B) ...

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

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

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

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

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

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