How would I evaluate the integral: $$I=\int{(\cos(x)\cosh(x)+\sin(x)\sinh(x)})\,dx$$ My thought was to use: $$\cos(ix)=\cosh(x)$$ and $$\sin(ix)=i\sinh(x)$$ or expand all four trig functions into exponentials but this was very messy
EDIT:
If I split this into two integrals where $I=I_1+I_2$ $$I_1=\int{cos(x)cosh(x)}dx$$ $$I_2=\int{sin(x)sinh(x)}dx$$
$$I_1=sin(x)cosh(x)-\int{sin(x)sinh(x)}dx$$ This second part is equal to $I_2$ so does that mean that $$I=sin(x)cosh(x)$$