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int (dx)/(sqrt(x-x^(2)))=...

`int (dx)/(sqrt(x-x^(2)))=`

A

`2sin^(-1) sqrt(x)+c`

B

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

C

`2x sin^(-1) x+c`

D

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

Text Solution

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The correct Answer is:
A
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SIA PUBLICATION-INDEFINITE INTEGRATION -PROBLEMS
  1. int (dx)/(x^(2)sqrt(4+x^(2)))=

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  2. If int sec^(2) x "cosec"^(4) x dx =-1/3 cos^(3)x + k tanx - 2cot x+c, ...

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  3. int (dx)/(sqrt(x-x^(2)))=

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  4. int(sqrt((a+x)/(a-x))) + sqrt((a-x)/(a+x))dx is equal to

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  5. If int (sin^(8)x-cos^(8)x)/(1-2sin^(2)cos^(2)x)dx=A sin 2x+B, then A=

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  6. int (1+cos4x)/(cotx-tanx)dx=

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  7. int (7x^(8)+8x^(7))/((1+x+x^(8))^(2))dx=f(x)+c rArr f(x)=

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  8. If f(n)(x) = log log…..log x(log is repeated n-times), then int (xf(1)...

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  9. int (1-cosx)"cosec"^(2)x dx=f(x)+c rArr f(x)=

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  10. int (dx)/((x+1)sqrt(4x+3))=

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  11. int(2-sin 2x)/(1-cos2x)e^(x) dx is equal to

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  12. If I(n) = int(sin^(n))dx, then nI(n)-(n-1)I(n-1) equals to

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  13. If int(e^(x))(1-sinx)/(1-cosx)dx=f(x) constant, then f(x) is equal to

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  14. If I(n)= intx^(n) e^(cx) dx for n ge 1, then c, I(n) + nI(n-1) is equa...

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  15. If inte^(x)(1+x) sec^(2)(xe^(x))dx = f(x) + constant, then f(x) is equ...

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  16. If int(e^(x)-1)/(e^(x)+1)dx = f(x)+c, then f(x) is equal to

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  17. int tan^(-1) (sqrt((1-x)/(1+x)))dx is equal to

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  18. int(sinx + 8 cosx)/(4 sinx + 6 cosx)dx is equal to

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  19. Assertion (A) (x^(2)-1)/(x^(2))e^(x^(2)+1)/x dx = e^(x^(2)+1)/x + c ...

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  20. If intsqrt(x/(a^(3)-x^(3)))dx = g(x)+c, then g(x) is equal to

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