Por favor me podrian ayudar con esto : Resolver las siguientes integrales enunciando claramente la técnica o propiedad usada.
En resumen
1) Note que<img src="https://tex.z-dn.net/?f=d%28e%5Ex%29%3De%5Exdx" /> <img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint%20%286x%5E2e%5Ex%29dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint%20%286x%5E2%29d%28e%5Ex%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BRecuerde%20...
1) Note que<img src="https://tex.z-dn.net/?f=d%28e%5Ex%29%3De%5Exdx" />
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint%20%286x%5E2e%5Ex%29dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint%20%286x%5E2%29d%28e%5Ex%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BRecuerde%20...%7D%20%5Cint%20u~dv%3Duv-%5Cint%20v~du%5C%5C%20%5C%5C%0AI%3D6x%5E2e%5Ex-%5Cint%20e%5Exd%286x%5E2%29%5C%5C%20%5C%5C%0AI%3D6x%5E2e%5Ex-%5Cint%20e%5Ex%5Ccdot%2012x~dx%5C%5C%20%5C%5C%0AI%3D6x%5E2e%5Ex-12%5Cint%20x~d%28e%5Ex%29%5C%5C%20%5C%5C%20%5C%5C%0AI%3D6x%5E2e%5Ex-12%5Cleft%5Bxe%5Ex-%5Cint%20e%5Ex%20~dx%5Cright%5D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D6x%5E2e%5Ex-12%28xe%5Ex-e%5Ex%29%2BC%5C%5C%20%5C%5C%0AI%3D6x%5E2e%5Ex-12xe%5Ex%2B12e%5Ex%2BC%5C%5C%20%5C%5C%0A%5Cboxed%7BI%3D%286x%5E2-12x%2B12%29e%5Ex%2BC%5C%5C%20%5C%5C%7D" />
2)
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint%20%5Ccos%5E4%20x%5Csin%5E3x~dx%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BNote%20que%20%7Dd%28%5Ccos%20x%29%3D-%5Csin%20x%20~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cint%20%5Ccos%5E4%20x%5Csin%5E2x%5Ccdot%28-%5Csin%20x%29~dx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cint%20%5Ccos%5E4%20x%5Csin%5E2x~d%28%5Ccos%20x%29%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cint%20%5Ccos%5E4%20x%281-%5Ccos%20%5E2x%29~d%28%5Ccos%20x%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BHaciendo%20%7Du%3D%5Ccos%20x%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cint%20u%5E4%281-u%5E2%29~du%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cint%20u%5E4-u%5E6~du%5C%5C%20%5C%5C%20%5C%5C%0AI%3D-%5Cdfrac%7Bu%5E5%7D%7B5%7D%2B%5Cdfrac%7Bu%5E7%7D%7B7%7D%2BC" />
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D-%5Cdfrac%7B%5Ccos%5E5x%7D%7B5%7D%2B%5Cdfrac%7B%5Ccos%5E7x%7D%7B7%7D%2BC%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BLuego%3A%7D%5C%5C%20%5C%5C%0A%5Cint%5Climits_%7B0%7D%5E%7B%5Cpi%2F2%7D%5Ccos%5E4%20x%5Csin%5E3x~dx%3D%5Cleft.%5Cleft%28-%5Cdfrac%7B%5Ccos%5E5x%7D%7B5%7D%2B%5Cdfrac%7B%5Ccos%5E7x%7D%7B7%7D%5Cright%29%5Cright%7C_%7B0%7D%5E%7B%5Cpi%2F2%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cint%5Climits_%7B0%7D%5E%7B%5Cpi%2F2%7D%5Ccos%5E4%20x%5Csin%5E3x~dx%3D%5Cdfrac%7B2%7D%7B35%7D%7D" />.
El método más sencillo consiste en realizar la división de los binomios : (2 x + 3) / (x + 2 ) = 2 - 1 / (x + 2) Los dos términos tienen integral inmediata. I = 2 x - Ln(x + 2) + C Saludos Herminio.
Hola lo hice en una hoja.
.
Intercambiar lados x + 1 / 2 >−1 Multiplicar ambos lados por 2 2(x + 1) / 2 >2(−1) Simplificar x + 1>−2 Restar 1 de ambos lados x + 1−1>−2−1 Simplificar x>−3 Multiplicar ambos lados por 2 2(x + 1) / 2.