Ubuntu – How to enable hardware video acceleration with an Intel graphics chipset on Ubuntu 17.10

It seems, that with Ubuntu 17.10 something has changed with the hardware video acceleration. It's not working properly anymore out-of-the-box with an Intel graphics chipset, because videos played in VLC are stuttering. The terminal shows the following, when opening a video:

$ vlc
VLC media player 2.2.6 Umbrella (revision 2.2.6-0-g1aae78981c)
[0000555baee879d8] core libvlc: VLC wird mit dem Standard-Interface ausgeführt. Benutzen Sie 'cvlc', um VLC ohne Interface zu verwenden.
Gtk-Message: GtkDialog mapped without a transient parent. This is discouraged.
[00007fcbd4008758] vdpau_avcodec generic error: unsupported codec 1211250229 or profile 1
Failed to open VDPAU backend libvdpau_i965.so: Kann die Shared-Object-Datei nicht öffnen: Datei oder Verzeichnis nicht gefunden
^CQObject::~QObject: Timers cannot be stopped from another thread

The same is true for Gnome's Video (Totem).

While installing Ubuntu Install third-party software was ticked on with an active internet connection.

Installing libvdpau-va-gl1 and rebooting also didn't help. I'm running Ubuntu on Xorg, not Wayland.

In Ubuntu 17.04 it was sufficient to install i965-va-driver and optionally vainfo. Now, in Ubuntu 17.10, vdpau files like libvdpau1 and vdpau-driver-all are also installed by default, although they are responsible for Nvidia's hardware acceleration.

According to vainfo everything is installed and detected properly:

$ vainfo
libva info: VA-API version 0.40.0
libva info: va_getDriverName() returns 0
libva info: Trying to open /usr/lib/x86_64-linux-gnu/dri/i965_drv_video.so
libva info: Found init function __vaDriverInit_0_40
libva info: va_openDriver() returns 0
vainfo: VA-API version: 0.40 (libva )
vainfo: Driver version: Intel i965 driver for Intel(R) Ivybridge Mobile - 1.8.3
vainfo: Supported profile and entrypoints
      VAProfileMPEG2Simple            : VAEntrypointVLD
      VAProfileMPEG2Simple            : VAEntrypointEncSlice
      VAProfileMPEG2Main              : VAEntrypointVLD
      VAProfileMPEG2Main              : VAEntrypointEncSlice
      VAProfileH264ConstrainedBaseline: VAEntrypointVLD
      VAProfileH264ConstrainedBaseline: VAEntrypointEncSlice
      VAProfileH264Main               : VAEntrypointVLD
      VAProfileH264Main               : VAEntrypointEncSlice
      VAProfileH264High               : VAEntrypointVLD
      VAProfileH264High               : VAEntrypointEncSlice
      VAProfileH264StereoHigh         : VAEntrypointVLD
      VAProfileVC1Simple              : VAEntrypointVLD
      VAProfileVC1Main                : VAEntrypointVLD
      VAProfileVC1Advanced            : VAEntrypointVLD
      VAProfileNone                   : VAEntrypointVideoProc
      VAProfileJPEGBaseline           : VAEntrypointVLD

The hardware is also fine:

$ lspci -nnk | grep -i VGA -A2
00:02.0 VGA compatible controller [0300]: Intel Corporation 3rd Gen Core processor Graphics Controller [8086:0166] (rev 09)
    Subsystem: Toshiba America Info Systems 3rd Gen Core processor Graphics Controller [1179:fb31]
    Kernel driver in use: i915

Any ideas how to solve this?