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If f(x) = frac{sin^(-1)x}{sqrt (1-x^2)},...

If f(x) = `frac{sin^(-1)x}{sqrt (1-x^2)}`, `g(x)=e^(sin^(-1)x)`, then `int` `f(x)g(x)` dx =........................ A) `e^(sin^(-1)x) (sin^(-1)x-1) + c` B) `e^( sin^(-1)x) (1- sin^(-1)x) + c` C) `e^(sin^(-1)x) (sin^(-1)x+1) + c` D) `-e^(sin^(-1)x) (sin^(-1)x-1) + c`

A

e^(`sin^(-1)`x)` (`sin^(-1)x`-1) + c

B

e^( `sin^(-1)`x)` (1- `sin^(-1)x`) + c

C

e^(`sin^(-1)`x)` (`sin^(-1)x`+1) + c

D

e^(`sin^(-1)`x)` (`sin^(-1)x`-1) + c

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CHETANA PUBLICATION-Indefinite Integration-Exercise
  1. int tan(sin^(-1) x) dx=........... A) (1-x^2)^(1/2) + c B) -(1-x^2)^...

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

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

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

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

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

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

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

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

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  11. 2 int frac{cos^2 x - sin^2 x}{cos^2 x + sin^2 x} dx=............ A) s...

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

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

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

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

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

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

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

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

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

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