Thread: Which identity is used here?

Hello,
When I solved $\int e^{2x}*\cosh(x)dx$, I got the answer $(\frac{-\sinh(x)}{3}+\frac23\cosh(x))*e^{2x}+C$. But the answer provided is $\frac{e^{3x}}{6}+\frac{e^x}{2}+C$.Both answers are equal. I want to know which identity is used for making both of them equivalent?

No identities. Just definitions.

$$\sinh x \stackrel{\text{def}}{=} \dfrac{e^x-e^{-x}}{2}$$

$$\cosh x \stackrel{\text{def}}{=} \dfrac{e^x+e^{-x}}{2}$$