Question

integral of cos(x)sin(x)/cos^4(x)+1

Answer 1

let u = cos(x) and du = -sin(x) dx

\[-\int\limits_{}^{}\frac{ u }{ u^4 + 1 }du\]
let v = u^2 dv = 2u du;

\[-\frac{ 1 }{ 2 } \int\limits_{}^{}\frac{ dv }{ v^2 + 1 } = -\frac{ 1 }{ 2 }\tan^{-1}(v) = -\frac{ 1 }{ 2 }\tan^{-1}(u^2) = -\frac{ 1 }{ 2 }\tan^{-1}(\cos^2(x)) + C\]

Answer 2

thanks so much