How toIntegrate 7/(e^9x-13) dx?

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Answer 1 · 2018-03-31T19:08:00

$I=7/11*ln|(e^(9x)-13)/e^(9x)|+c$

$I=int7/(e^(9x)-13)dx$

We take,

$e^(9x)=u=>e^(9x)(9)dx=du$

$I=7/9int(9e^(9x))/(e^(9x)(e^(9x)-13))dx$

$=7/9int1/(u(u-13))du$

$=7/9*1/13int((u-(u-13))/(u(u-13)))du$

$=7/9*1/13int(1/(u-13)-1/u)du$

$=7/117[ln|u-13|-ln|u|]+c$

$=7/117*ln|(u-13)/u|+c...to$ where, $u=e^(9x)$

$=>I=7/117*ln|(e^(9x)-13)/e^(9x)|+c$