3-t-11-6-t-11-dt-collected-problem-

Question Number 124742 by TANMAY PANACEA last updated on 05/Dec/20

\int \frac{3^{t} + 11}{6^{t} + 11} d t c o l l e c t e d p r o b l e m

Commented by MJS_new last updated on 05/Dec/20

I get to this point :

\frac{3^{t} + 11}{6^{t} + 11} = \frac{1}{2^{t}} + \frac{11}{6^{t} + 11} - \frac{11}{2^{t} (6^{t} + 11)} =

= \frac{1}{2^{t}} + \frac{6^{t} + 11}{6^{t} + 11} - \frac{6^{t}}{6^{t} + 11} - \frac{11}{2^{t} (6^{t} + 11)} =

= \frac{1}{2^{t}} + 1 - \frac{6^{t}}{6^{t} + 11} - \frac{11}{2^{t} (6^{t} + 11)}

\int \frac{d t}{2^{t}} + \int d t - \int \frac{6^{t}}{6^{t} + 11} d t = - \frac{1}{2^{t} \ln 2} + t - \frac{\ln (6^{t} + 11)}{\ln 6}

but no idea for - 11 \int \frac{d t}{2^{t} (6^{t} + 11)}

Commented by MJS_new last updated on 05/Dec/20

maybe the hypergeometric function is

possible but I^{'} m not good at using it \dots

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