Question

Please help me get started on the following integration (click to see)...

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ \cos ^{2}x }\]

Answer 2

Well we do know that \(\frac{d}{dx}\tan(x)=\frac{1}{\cos^2(x)}\)
So we can use the relationship of:
\[F(x)=\int{f(x)}\]
\[\frac{d}{dx}F(x)=f(x)\]
\(F(x)=\tan(x)\)
\(f(x)=\frac{1}{\cos^2(x)}\)
\[\frac{d}{dx}\tan(x)=\frac{1}{\cos^2(x)}\]
\[\therefore:\phantom{spc}\tan(x)=\int{\frac{1}{\cos^2(x)}}\]