Q. 174.0( 4 Votes )

Evaluate :<

Answer :

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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