Galera, po gentileza, me ajudem a resolver essa questão de integral.

∫[tan²(x)cot²(x)]²dx = cot^4(x)tan^4(x)

cot = cosx/senx    ---> cot = 1/tg(x)

cot^4(x)tan^4(x) = 1/tg(x) tg(x)

\(=\int \:1dx\)

\(\int adx=ax\)

\(=1\cdot \:x\)

\(=x \)

\(=x+C\)

\(\Longrightarrow \int (\tan^2x \cdot \cot^2x)^2 \, dx\)

\(\Longrightarrow \int (\tan^2x \cdot {1 \over \tan^2x } )^2 \, dx\)

\(\Longrightarrow \int (1 )^2 \, dx\)

\(\Longrightarrow \int dx\)

\(\Longrightarrow \fbox {$ x+c $}\)

Sendo \(c\) uma constante qualquer.