'I gotta' is grammatically incorrect. It is more of a spoken form. If you want to say this with proper grammar, the equivalent would be, 'I have got to' or 'I've got to'. In the spoken form, 'got to' is shortened to 'gotta' and the word 'have' is dropped.
Learn English speaking much FASTER by downloading the TalkEnglish Offline Package and submerge yourself with over 8,000 audio files and over 800 pages of lessons! Then you can study without Internet connection and also listen to audio files using your MP3 player at any time. Go to the English Download page and download today!