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int frac{1}{x+x^5} dx = f(x) +c, then in...

`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

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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int frac{x+1}{x^2 + 5x + 6} dx=............ A) log(x+2) +2 log(x+3) + c B) log(x+2) - 2 log(x+3) + c C) -log(x+2) - 2 log(x+3) + c D) -log(x+2) + 2 log(x+3) + c

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

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{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

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

CHETANA PUBLICATION-Indefinite Integration-Exercise
  1. Integrate the following w.r.t. x: int frac{x}{(x-1)(x^2+1)} dx

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  2. int frac {1+x+sqrt (x+x^2)}{sqrt x + sqrt (1+x)} dx = .......... A) (...

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  3. int frac{1}{x+x^5} dx = f(x) +c, then intfrac{x^4}{x+x^5} dx = ..........

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  4. int frac{log (3x)}{xlog(9x)} dx = ............. (A) log(3x) - log(9x)...

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  5. int frac{sin^mx}{cos^(m+2)x} dx=.............. A) frac{tan^(m+1)x}{m+...

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

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

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

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

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

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

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

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

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

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  16. 2 int frac{cos^2 x - sin^2 x}{cos^2 x + sin^2 x} dx=............ A) s...

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

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

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

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

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