निम्नलिखित समाकलनों को ज्ञात कीजिए:
(i) `int (x^(3)-1)/x^(2) dx` (ii) `int (x^(2/3)+1)dx`
(iii) `int(x^(2/3)+2ex-1/x)dx`

Explanation

`int (x^(3)-1)/x^(3) dx= int x^(3)/x^(2)dx- int 1/x^(2) dx`
`=int x dx- int x^(-2) dx`
`=x^(1+1)/(1+1) - x^(-2+1)/(-2+1)`
`=1/2 x^(2)+x^(-1)`
`=1/2 x^(2)+1/x +c`.
(ii) `int(x^(2/3)+1) dx=int x^(2/3) dx+1int dx`
`=x^(2/3+1)/(2/3+1)+x+c`
`=x^(5/3)/(5//3)+x+c`
`=3/5 x^(5/3)+x+c`.
(iii) `int(x^(2/3)+2e^(x)-1/x)dx= int x^(2/3)dx+2int e^(x)dx-int 1/x dx`
`=x^(2/3+1)/(2/3+1)+2e^(x)-log|x|+c`
`=3/5 x^(5/3)+2e^(x)-log |x|+c`.