Question

integral de substituição [cos(6w^2+5)] .24w dw

Answer 1

$Integral:\\\\ F_{(w)} = \displaystyle \int cos(6w^2+5)\ .\ 24w\ dw\\\\\\ Integrando\ por\ substitui\c{c}\~ao:\\\\ F_{(w)} = 24\displaystyle \int cos(\underbrace{6w^2+5})\ .\ w\ dw\\ \ ~~~~~~~~~~~~~~~~~~~~~~~~~~~u\\\\ u=6w^2+5\\\\ du=12w.dw\ \ \Rightarrow\ \ w.dw=\frac{du}{12}\\\\\\ Substituindo:\\\\ F_{(w)} = 24\displaystyle \int cos(u)\ .\ \frac{du}{12}\\\\ F_{(w)} = \dfrac{24}{12}\displaystyle \int cos(u)\ .\ du\\\\ F_{(w)} = 2\displaystyle \int cos(u)\ .\ du\\\\ F_{(w)} = 2\sin(u)$

$\boxed{F_{(w)} = 2\sin(6w^2+5)+constante}$


Espero ter ajudado.
Bons estudos!