Respuesta :

Nayefx

Answer:

[tex] \huge \boxed{\red{ \boxed{ - \cos(x) + C}}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • integration
  • PEMDAS

tips and formulas:

  • [tex] \tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) } [/tex]
  • [tex] \sf \displaystyle \int \sin(x) \: dx = - \cos(x) + C[/tex]

let's solve:

  1. [tex] \sf \: rewrite \: \tan( \theta) \: as \: \dfrac{ \sin( \theta) }{ \cos( \theta) } : \\ = \displaystyle \int \: \frac{ \sin(x) }{ \cos(x) } \cos(x) \: dx \\ = \displaystyle \int \: \frac{ \sin(x) }{ \cancel{\cos(x) }} \: \cancel{ \cos(x)} \: dx \\ = \displaystyle \int \: \sin(x) \: dx[/tex]
  2. [tex] \sf \: use \: the \: formula : \\ \sf \displaystyle - \cos(x) [/tex]
  3. [tex] \sf add \: constant : \\ - \cos(x) + C[/tex]

[tex]\text{And we are done!}[/tex]

Answer:

-cosx+c is your answer

Step-by-step explanation:

[tex] \displaystyle \int \: \tan(x) \cos(x) \: dx[/tex]

[tex] \displaystyle \int \: \sin \: x \div \cos(x) \times \cos(x) dx [/tex]

[tex] \displaystyle \int \: sinx \: dx \\ - \cos(x) + c[/tex]