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int 5^(x+tan^(-1)x)*((x^(2)+2)/(x^(2)+1)...

`int 5^(x+tan^(-1)x)*((x^(2)+2)/(x^(2)+1))dx`.

Text Solution

Verified by Experts

Let `x+tan^(-1)x=t`
` :. (1+(1)/(x^(2)+1))dx=dt " or "((x^(2)+2)/(x^(2)+1))dx=dt`
` :. int 5^(x+tan^(-1)x)*((x^(2)+2)/(x^(2)+1))dx=int 5^(t) dt`
`=(5^(t))/(log_(e)5)+c`
`=(5^(x+tan^(-1)x))/(log_(e)5)+c`
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