Exercício
$\frac{1}{1+\cos^2}+\frac{1}{1+\sec^2a}$
Derivada desta função
$\frac{d}{da}\left(\frac{1}{1+\cos\left(a\right)^2}+\frac{1}{1+\sec\left(a\right)^2}\right)=\frac{2\cos\left(a\right)\sin\left(a\right)}{\left(1+\cos\left(a\right)^2\right)^2}+\frac{-2\sec\left(a\right)^2\tan\left(a\right)}{\left(1+\sec\left(a\right)^2\right)^2}$
Veja solução passo a passo
Integral desta função
$\int\left(\frac{1}{1+\cos\left(a\right)^2}+\frac{1}{1+\sec\left(a\right)^2}\right)da=\frac{2a+a\sec\left(a\right)^2+a\cos\left(a\right)^2}{\left(1+\cos\left(a\right)^2\right)\left(1+\sec\left(a\right)^2\right)}+C_0$
Veja solução passo a passo