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Question
The value of integral `int1/([(x-1)^3(x+2)^5]^(1/4)) dx` is ______.
Options
`4/3((x-1)/(x+2))^(1/4)+c`
`4/3((x+1)/(x+2))^(1/4)+c`
`4/3((x+1)/(x-2))^(1/4)+c`
`4/3((x-1)/(x-2))^(1/4)+c`
MCQ
Fill in the Blanks
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Solution
The value of integral `int1/([(x-1)^3(x+2)^5]^(1/4)) dx` is `underline(4/3((x-1)/(x+2))^(1/4)+c)`.
Explanation:
Put `(x-1)/(x+2)=t`
`=>1/(x+2)^2 dx=1/3dt`
`therefore int1/[(x-1)^3(x+2)^5]^(1/4) dx`
`=int 1/((x-1)^(3/4)(x+2)^(-3/4)(x+2)^2) dx`
`=1/3int t^(-3/4) dt`
`=1/3*t^(1/4)/(1/4)+c`
`=4/3((x-1)/(x+2))^(1/4)+c`
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