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find ∫42 x/(x2+1) dx - Mathematics

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find `∫_2^4 x/(x^2 + 1)dx`

 
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Solution

`∫_2^4 x/(x^2 + 1)dx`

`Put x^2+1=t`

`2xdx=dt`


Now, 
`1/2∫_5^17 1/tdt`

`⇒1/2log t_5^17`

`⇒1/2(log 17−log 5)`

`⇒1/2log (17/5)`

Concept: Evaluation of Definite Integrals by Substitution
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