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int 1/((x-1)^3(x+2)^5)^(1/4)dx is equal ...

`int 1/((x-1)^3(x+2)^5)^(1/4)dx` is equal to

A

`(4)/(3)((x-1)/(x+2))^(1//4)+C`

B

`(4)/(3)((x+2)/(x-1))^(1//4)+C`

C

`(1)/(3)((x-1)/(x+2))^(1//4)+C`

D

`(1)/(3)((x+2)/(x-1))^(1//4)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(1)/([(x-1)^(3)(x+2)^(5)]^(1//4))dx`
`=int(1)/(((x-1)/(x+2))^(3//4)(x+2)^(2))dx`
`=(1)/(3)int(1)/(t^(3//4))dt("put "(x-1)/(x+2)=t rArr (3)/((x+2)^(2))dx=dt)`
`=(1)/(3)((t^(1//4))/((1)/(4)))+C=(4)/(3)t^(1//4)+C=(4)/(3)((x-1)/(x+2))^(1//4)+C`
`=(1)/(3)((t^(1//4))/((1)/(4)))+C=(4)/(3)t^(1//4)+C=(4)/(3)((x-1)/(x+2))^(1//4)+C`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-INTEGRATION -PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. int((1+x)sinx)/((x^(2)+2x)cos^(2)x-(1+x)sin 2x)dx

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  2. int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx

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  3. int 1/((x-1)^3(x+2)^5)^(1/4)dx is equal to

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  4. intcos2thetalog((costheta+sintheta)/(costheta-sintheta))=

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  5. int tan(x-alpha).tan(x+alpha).tan 2x dx is equal to

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  6. int[(sqrt(x^2+1)(ln(x^2+1)-2lnx)))/(x^4) dx

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  7. int(dx)/(sqrt(sin^3xsin(x+alpha)))

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  8. If int(dx)/(root3(sin^(11)xcosx))=-[(3)/(8)f(x)+(3)/(2)g(x)]+C, then

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  9. int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx is equal to

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  10. If I=int(sinx+sin^3x)/(cos2x) dx=Pcosx+Q log|f(x)|+R,then

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  11. int(2)/((2-x)^(2))root3((2-x)/(2+x))dx is equal to

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  12. int(x^(2)+cos^(2)x)/(x^(2)+1)."cosec"^(2)xdx is equal to

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  13. In the integral int(cos 8x+1)/(cot 2x-tan 2x)dx=A cos 8x+k, where k...

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  14. int(dx)/(a^(2)sin^(2)x+b^(2)cos^(2)x) is equal to

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  15. If int(sqrt(cotx))/(sinxcosx)dx=Psqrt(cotx)+Q, then the value of P is

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  16. inte^(e^(e^(x))).e^(e^(x)).e^(x)dx=....+C

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  17. int"cosec"(x-a)"cosec"xdx is equal to

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  18. If f((3x-4)/(3x+4))=x+2, then int f(x)dx is equal to

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  19. int(dx)/(cos^(3)xsqrt(2sin 2x)) is equal to

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  20. Let int(x^(2))/(sqrt(1-x))dx=psqrt((1-x))(3x^(2)+4x+8), then value of ...

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