Evaluate the following integrals:

Assume $\cos ^{2} x=t$

$d\left(\cos ^{2} x\right)=d t$

$-2 \sin x \cos x d x=d t$

$-\sin 2 x \cdot d x=d t$

Substituting $\mathrm{t}$ and $\mathrm{dt}$

$\Rightarrow \int e^{t} \cdot d t$

$\Rightarrow e^{t}+c$

But $t=\cos ^{2} x$

$\Rightarrow e^{\cos 2 x}+c$