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Evaluate: (i) intsqrt(x)(3-5x)\ dx (ii...

Evaluate:
(i) `intsqrt(x)(3-5x)\ dx`
(ii) `int((x+1)(x-2))/(sqrt(x))\ dx`

Text Solution

Verified by Experts


(i) `intsqrt(x)(3-5x)\ dx`

`=int(3sqrt(x)-5x)\dx`

`=2x^(3/2)-(5x^(2))/(2)+C`

(ii) `int((x+1)(x-2))/(sqrt(x))\ dx`

`=int((x^2-x-2))/(sqrt(x))\dx`

`=int(x^(3/2)-sqrt(x)-2x^(-1/2))\dx`

`=(2x^(5/2))/(5)-(2x^(3/2))/(3)-4x^(1/2)+C`

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