Ok

you are sure about your simplification right I will tell you how to integrate the terms

the first integral the you can put the constant C out of the integration

sinh^2x = ( e^x - e^-x)^2/4 = ( e^2x - 2 + e^-2x )/4 since sinhx=e^x/2 - e^-x/2

now you can integrate ( e^2x - 2 + e^-2x )/4 = ( e^2x/2 -2x + e^-2x/-2 )/4

the second integral sin^2x = ( 1 - cos2x )/2 since " cos2x=1-sin^2x "

now you can integrate ( 1 - cos2x )/2 = ( x - sin2x/2 )/2

the third integral cosh^2x like the sinhx but

coshx = ( e^x + e^-x )/2

cosh^x = e^2x +2 + e^-2x )/4 I leave it for you to integrate

fourth

cos^2x = ( cos2x + 1)/2 since " cos2x = 2cosx - 1 " I leave it for you