How do you integrate #\int _ { - 9} ^ { 9} \frac { 3e ^ { x } } { \sinh ( x ) + \cosh ( x ) } d x#?

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Answer 1 · 2017-06-22T17:28:45

#54#

#int_(-9)^(9)(3e^x)/(sinhx+coshx)dx#

change the hyperbolic functions to their respective exponential definitions

#=int_(-9)^(9)(3e^x)/(1/2(e^xcancel(-e^(-x)))+1/2(e^x+cancel(e^(-x))))dx#

#=int_(-9)^(9)(3cancel(e^x))/(cancel(e^x))dx#

#=int_(-9)^(9)3dx#

#=[3x]_(-9)^(9)#

#=3{[x]_(-9)^(9)}#

#=3(9- -9)#

#=3xx18=54#