Verified answer

∫ dx/(7^x+1) =

substitute 7^x = u

x LN 7 = LN u

dx = du/(uLN 7)

∫dx/(7^x+1) = (1/LN 7)∫du/(u(u + 1)) =

= (1/LN 7)[ ∫du/u - ∫du/(u + 1)] =

= (1/LN 7)( LN(u) - LN(u + 1) ) + C =

= (1/LN 7)( LN( 7^x) - LN( 7^x + 1) ) + C =

= ( LN( 7^x)/LN 7) - (LN( 7^x + 1)/LN 7) + C =

= x - log₇(7^x + 1) + C =

enable U = lnx^2 dv=x dU= 2/x v= x^2/2 indispensable xln(x^2)dx = (x^2.lnx^2) - indispensable (2/x)(x^2/2) dx = (x^2.lnx^2) - indispensable (x) = (x^2.lnx^2) - x^2/2 + C it is waht you're assume to get bro