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Evaluate: inte^xx/((x+1)^2)\ dx...

Evaluate: `inte^xx/((x+1)^2)\ dx`

Text Solution

Verified by Experts

`I=int frac{d x}{(e^{x}-1)^{2}}`
put `e^{x}=t`
` therefore d x=d t`
` therefore=frac{d x}{e^{x}}=frac{d t}{e^{x}}=frac{d t}{t}`
` I frac{d t}{t(t-1)^{2}}`
` I=int frac{t-(t-1)}{t(t-1)^{2}} d t`
` I=int[frac{1}{(t-1)^{2}}-frac{1}{t(t-1)}] d t`
` I=int frac{1}{(t-1)^{2}} d t-int frac{t-(t-1)}{t(t-1)} d t`
` ...
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