integral of xcosh3x2sinhx2dxSolutioncosh x ex e12 differnt

Solution

cosh x = (e^x + e^(-1))/2 differntiation of cosh x = (e^x -e^(-1))/2 =sinh x

let cosh^3(x^2) = t

differntiating with respect to x

we get

2x*3cosh^2(x^2) *sinh x^2 = dt/dx

hence [x*3cosh^2(x^2) *sinh x^2]dx =dt/2

putting this in the expression of which we have to find integral

we get (t*dt/2) =t^2 /4 + c

ie [cosh^6(x^2)]/4 +c