Question

Qual a integral de 2 senx - 5 cos x/cos x dx?

Answer 1

Boa noite Silene!

Solução!



$\displaystyle \int 2sen(x)- \frac{5cos(x)}{cos(x)}dx\\\\\\\ 2\displaystyle \int sen(x)dx- 5\displaystyle \int\frac{cos(x)}{cos(x)}dx\\\\\\\ 2\displaystyle \int sen(x)dx- 5\displaystyle \int(1)dx\\\\\\\ Olhando~~na~~ tabela~~de~~integrais~~vai~~ encontrar:\\\\\\\\ \displaystyle \int sen(x)dx=-cos(x)\\\\\\ (-2cos(x)-5x+c)\\\\\\\\\\\\ \boxed{Resposta:\displaystyle \int 2sen(x)- \frac{5cos(x)}{cos(x)}dx=(-2cos(x)-5x+c)}$

Boa noite!
Bons estudos!

Answer 2

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$\displaystyle\sf\int\bigg(2 sen(x)-\dfrac{5\diagdown\!\!\!\!cos(x)}{\diagdown\!\!\!\!cos(x)}\bigg)~dx\\\sf=-2cos(x)-5x+k$