Evaluate :<

Substitute u = 5x + 1

By using partial fraction decomposition

v = ln(u - 1) du = (u - 1)dv

Applying power rule

But v = ln(u - 1)

=

Now we need to solve

Integrating by parts we get

=

Now to solve

Now to solve

Substitute v = 1 – u du = - dv

=

= Li3(v)

= Li3(1 - u)

Finally, Substituting all the integrals back we get

=

Undoing Substitution u = 5x + 1 use:

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

=

The Problem is solved:

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