I'm a difficulty in Ubuntu. I need to save a figure work of Inkscape in png or jpeg format, however, this figure work needs to be 400dpi resolution. I saved the jpeg using output pro inkscape plugin, but I can not insert the image into LibreOffice Writter (I think the reason is that the image was very extensive, but I am obliged to do so, because my university has the using standard figures 400dpi).
I'm actually surprised they're asking you to take a vector drawing such as those produced by Inkscape and convert it to a raster image because vector images are resolution-independent and therefore produce excellent print output anyway, so you may want to start by double-checking they really want you to do that. The rest of my answer will assume that you have checked and the university really do want an image.
Your problem here is probably more one of trying to force LibreOffice to do something it isn't designed for - namely prepare output for a high-quality printing press rather than a standard home or office printer. I prepare output for press regularly and, if your university guidelines permit, you should really do this on desktop publishing (DTP) software (your university probably should allow this if they're asking for 400 dpi images). I suspect, however, that your university might not be asking you to do so much. It would be more normal for someone in their position (as a publisher) to ask you (as a content producer) to provide the text and images separately for them to prepare in the DTP package of their choice.
If they are set on asking for a complete, press-ready document from you then I recommend downloading scribus from the software centre and working through the scribus tutorial. Once you've done that you'll know how to import your text and your image in a way that will ensure high-quality press output. You can then export a press-ready PDF to submit to your university.
I recommend you save your figures as EPS instead - you can do this from the Save As... menu in Inkscape. Academic publishers like TIFF for bitmaps and EPS for vector art, in my experience.
This means the publisher can scale the image to any size they like, without jaggies.