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Integrate:   `int` `(sqrt(x)/(x^2+x))` ` ` ` `   ` `

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chainrule | (Level 1) eNoter

Posted July 17, 2013 at 12:47 AM via web

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Integrate:

 

`int` `(sqrt(x)/(x^2+x))`

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 17, 2013 at 1:07 AM (Answer #1)

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Let ;

`x = tan^2t`

`dx = 2tantsec^2tdt`

`sqrtx/(x^2+x) `

`= (sqrt(tan^2t))/(tan^4x+tan^2t)`

`= (tant)/(tan^2t(1+tan^2t))`

`= 1/(tantsec^2t)`

`intsqrtx/(x^2+x)dx`

`= int1/(tantsec^2t)xx2tantsec^2tdt`

`= int2dt`

`= 2t+C` Where C is a constant.

`= 2tan^(-1)sqrtx+C`

So the answer is `intsqrtx/(x^2+x)dx = 2tan^(-1)sqrtx+C`

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