Question

The value of integral `int1/([(x-1)^3(x+2)^5]^(1/4))  dx` is ______.

विकल्प

• `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`

Answer 1

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`