Evaluate :  [CBSE 2016]

Substitute u = 5^x + 1

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By using partial fraction decomposition

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v = ln(u - 1) → du = (u - 1)dv

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Applying power rule

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But v = ln(u - 1)

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Now we need to solve

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Integrating by parts we get

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Now to solve

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Now to solve

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Substitute v = 1 – u → du = - dv

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= Li₃(v)

= Li₃(1 - u)

Finally, Substituting all the integrals back we get

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Undoing Substitution u = 5^{x +} 1 use:

ln(5^x + 1 - 1) = ln(5)x

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The Problem is solved:

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