I have a long integral and broken it up and solved everything besides $\displaystyle \int tanh 7x dx$
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Originally Posted by circuscircus I have a long integral and broken it up and solved everything besides $\displaystyle \int tan 7x dx$ a simple substitution of $\displaystyle t = 7x$ will do
Originally Posted by Jhevon a simple substitution of $\displaystyle t = 7x$ will do Yea understood but the problem is my book gives the integrals for only sinh, cosh,sech^2,csc^2,sech, and csch but not tanh nor coth
Originally Posted by circuscircus Yea understood but the problem is my book gives the integrals for only sinh, cosh,sech^2,csc^2,sech, and csch but not tanh nor coth oh, you changed the question. note that $\displaystyle \tanh x = \frac {\sinh x}{\cosh x}$ and it is still an easy substitution problem
$\displaystyle Dx tanh 7x$ $\displaystyle = Dx \frac{sinh(7x)}{cosh(7x)}$ use quotient rule $\displaystyle = \frac{7cosh(7x)cos(7x) - 7sinh(7x)sinh(7x)}{cosh(7x)^2}$ so is it like this?
Originally Posted by circuscircus $\displaystyle Dx tanh 7x$ $\displaystyle = Dx \frac{sinh(7x)}{cosh(7x)}$ use quotient rule $\displaystyle = \frac{7cosh(7x)cos(7x) - 7sinh(7x)sinh(7x)}{cosh(7x)^2}$ so is it like this? ......are you confused about something? or did you type the wrong question originally? you should be finding the integral, not taking the derivative
OH man sorry I was out of it Yea, how would I solve the integral of e^x-e^-x / e^x+e^-x
Originally Posted by circuscircus OH man sorry I was out of it Yea, how would I solve the integral of e^x-e^-x / e^x+e^-x there is no need to write the formulas that way. just use the substitution $\displaystyle u = \cosh x$
u = coshx du = sinhx 1/u du ln |u| + C ln |coshx|+c Thanks!
Originally Posted by circuscircus u = coshx du = sinhx 1/u du ln |u| + C ln |coshx|+c Thanks! not quite. remember, we are dealing with $\displaystyle \tanh {\color {red}7}x$ but i think you have the idea
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