After reading a textbook about integrals, my curiosity sparks about the following integral:

$$\int_0^\infty e^{-t} \log(\cos^2 t)\, \mathrm dt$$

How to evaluate a closed form of this integral ? My bet is to use the Cauchy Integral Theorem of Residues or the Laplace Transform.

After reading a textbook about integrals, my curiosity sparks about the following integral: $$ \int_{0}^{\infty}{\rm e}^{-t} \log\left(\cos^{2}\left(t\right)\right){\rm d}t $$

• How to evaluate a closed form of this integral ?.
• My bet is to use the Cauchy Integral Theorem of Residues or the Laplace Transform.

After reading a textbook about integrals, my curiosity sparks about the following integral:

$\int_0^\infty\!{e^{-t} \log(\cos^2 t) }\,dt$

How to evaluate a closed form of this integral ? My bet is to use the Cauchy Integral Theorem of Residues or the Laplace Transform.

After reading a textbook about integrals, my curiosity sparks about the following integral:

$$\int_0^\infty e^{-t} \log(\cos^2 t)\, \mathrm dt$$

How to evaluate a closed form of this integral ? My bet is to use the Cauchy Integral Theorem of Residues or the Laplace Transform.