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int ((1)/(sqrt(x+2)-sqrt(x)))dx=....+c...

`int ((1)/(sqrt(x+2)-sqrt(x)))dx=....+c`

A

`(3)/(2)(x+2)^((3)/(2))+(2)/(3)x^((3)/(2))`

B

`(3)/(2)(x+2)^((1)/(2))+(2)/(9)x^((1)/(2))`

C

`(3)/(2)(x+2)^((3)/(2))+(2)/(9)x^((3)/(2))`

D

`(2)/(9)(x+2)^((3)/(2))+(2)/(9x`

Text Solution

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The correct Answer is:
D
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KUMAR PRAKASHAN-INTEGRALS -MULTIPLE CHOICE QUESTIONS(MCQS)
  1. int(x^((1)/(2)))/(sqrt(1-x^(3)))dx=(2)/(3)go f(x)+c then....

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  2. int (dx)/(sqrt(1-x))=..

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  3. int ((1)/(sqrt(x+2)-sqrt(x)))dx=....+c

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  4. intsqrt((a-x)/(a+x))dx=....+c

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  5. int(x^(2)+1)/(x^(4)-x^(2)+1)dx=...+c

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  6. Find int[sqrt(cotx)+sqrt(tanx)]dx

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  7. int(e^(exlog(e)x)+(log(e)x)(e^(exlog(e)x)))dx=...+c

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  8. int((x-1)^(2))/((x^(2)+1)^(2))dx=tan^(-1)x+f(x)+c then f(x)=....

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  9. int(1)/(e^(x)+1)dx=....

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  10. int(x^(3)+4x-3)/(x^(2)+4)dx=Ax^(2)+B "tan"^(-1)(x)/(2)+c then A+B=... ...

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  11. Integration using trigonometric identities : int (cos^(8)x-sin^(8)x)...

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  12. If Integration using rigonometric identities : int(dx)/(sqrt(sin^(3)...

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  13. Integration using rigonometric identities : (d)/(dx)g(x)=g(x) and g(...

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  14. Integration using rigonometric identities : int(sin theta)/(cos3 the...

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  15. Integration using rigonometric identities : int sin(101x)*sin^(99)x ...

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  16. Integration using rigonometric identities : int sin 4x*e^(tan^(2)x)d...

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  17. Integration using trigonometric identities : int (d theta)/(sin thet...

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  18. Integration using rigonometric identities : int(sin 2x)/(sin^(4)x+co...

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  19. Integration using rigonometric identities : int cos^(5)xdx=....

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  20. Integration using rigonometric identities : int sec x tan^(3)x dx=.....

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