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Evaluate: int5^(x+t a n^(-1)x)((x^2+2)/...

Evaluate: `int5^(x+t a n^(-1)x)((x^2+2)/(x^2+1))dx`

Text Solution

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`t=x+tan^-1x`
`=>dt=(1+1/(1+x^2))dx=((x^2+2)/(1+x^2))dx`
`int5^(x+t a n^(-1)x)((x^2+2)/(x^2+1))dx=int5^tdt`
Let `u=5^t`
`impliesdu=5^tlog5dt`
`=(1/log5)int du`
`=(1/log5)u+c`
`=(1/log5)5^t+c` where `u=5^t`
...
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