Takeuchi started for the Finnish club Puijon Hiihtoseura until 2006 , and in 2007 he moved to the Japanese factory team Kitano Kensetsu in Nagano . His first appearance in the Ski Jumping Continental Cup was on January 15, 2005 in Sapporo . This season he reached 164th place with two points and 49th place in the following season with 115 points. On November 24, 2006, the first use in the ski jumping world cup took place in Kuusamo . In the Continental Cup he reached the 39th place with 162 points this season . At the Ski Jumping World Cup 2006/07 he won his first World Cup points and finished 65th with 16 points. In the next season he finished 28th with 180 points.
At the 2010 Winter Olympics in Vancouver , Takeuchi was eliminated in the individual jumping on the normal hill as 34th and on the large hill as 37th after the first round. With the Japanese team, he finished fifth. On January 4, 2012, he was able to achieve third place in the jumping in Innsbruck as part of the Four Hills Tournament , and for the first time in his career he achieved a podium in an individual competition in the World Cup. In the final classification of the Four Hills Tournament he was ninth.
On September 23, 2012, he was able to win a jumping in this competition for the first time at the Summer Grand Prix in Almaty, Kazakhstan . He benefited from the fact that the jumping was canceled after the first round because of strong winds. He achieved his best World Cup result so far on February 13, 2013 when he finished second in Klingenthal as part of the 2013 FIS Team Tour .
On December 6, 2013, Takeuchi won the mixed team competition in Lillehammer together with Yūki Itō, Daiki Itō and Sara Takanashi, thus achieving his first World Cup victory. The following day he was able to set his best individual result in the individual jumping with second place behind Gregor Schlierenzauer . At the 2014 Winter Olympics in Sochi , he finished 24th in the individual competition on the normal hill and 13th on the large hill. In the team competition he won the bronze medal together with Reruhi Shimizu , Daiki Itō and Noriaki Kasai .
On September 21, 2014, he won his second Grand Prix event , like two years ago, he was victorious in Almaty. At the Nordic World Ski Championships in Falun in 2015 , he finished fifth on the normal hill in the individual competition and in the mixed team competition he won the bronze medal together with Sara Takanashi, Noriaki Kasai and Yūki Itō. On the large hill he was 24th in the individual and fourth with the team.
On February 21, 2016, he finished third in Lahti and achieved the fourth podium of his career in an individual World Cup competition. On August 28, 2016, he won his third Grand Prix competition in Hakuba . At the Nordic World Ski Championships 2017 in Lahti, he finished 20th in the individual competition on the normal hill. In the mixed team competition, he repeated the success of 2015 and again won the bronze medal together with Sara Takanashi, Yūki Itō and Daiki Itō. On the large hill he was 17th in the individual and seventh with the team.