Question

intergrate 4coshx-2sinh2x

Answer 1

4sinhx - cosh(2x) + C

Answer 2

$$\int(4\cosh x-2\sinh2x)\,dx=4\int\cosh x\,dx-2\int\sinh2x\,dx=4\sinh x-\cosh2x+C$$

Answer 3

note how nice hyperbolic functions are... $$\int\sinh x\,dx=\cosh x+C\\\int\cosh x\,dx=\sinh x+C$$in fact \(k\cosh x,k\sinh x\) are the solutions to \(y''=y\)