sin(ln(x)) < Integralrechnung < Analysis < Oberstufe < Schule < Mathe < Vorhilfe
|
Und das nächste Integralchen:
[mm] \int_{}{sin(ln(x))dx}
[/mm]
z=ln(x), [mm] x=e^z
[/mm]
z'=1/x
dx=xdz
[mm] \int_{}{xsin(z)dz}
[/mm]
[mm] \int_{}{e^zsin(z)dz}
[/mm]
[mm] =-cos(z)e^z+\int_{}{e^zcos(z)dz}
[/mm]
[mm] =-cos(z)e^z+sin(z)e^z-\int_{}{e^zsin(z)dz}
[/mm]
[mm] 2\int_{}{e^zsin(z)dz} [/mm] = [mm] -cos(z)e^z+sin(z)e^z
[/mm]
[mm] \int_{}{e^zsin(z)dz} =\frac{1}{2}(-cos(z)e^z+sin(z)e^z)
[/mm]
[mm] =\frac{1}{2}x(-cos(ln(x))+sin(ln(x)))
[/mm]
in Ordnung so?
|
|
| |
|
Hallo,
das sieht alles richtig aus!
Gruß Patrick
|
|
|
|
