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Eğitmen, trigonometrik integral hesaplamaları için yarım açı yöntemi (tanjant x/2 = t dönüşümü) konusunu anlatmaktadır.","Video, yarım açı yönteminin temel prensiplerini açıklayarak başlıyor ve sinx, cosx ve dx ifadelerinin t değişkeni cinsinden nasıl yazılacağını gösteriyor. Ardından, bu yöntemin sekant ve kosekant fonksiyonlarının integral hesaplamalarında nasıl uygulanacağını adım adım örneklerle açıklıyor. Özellikle ∫dx/(1+sinx) ve ∫dx/(1+cosx) gibi integral problemlerinin çözümünde tan(x/2) dönüşümünün nasıl kullanıldığını detaylı şekilde göstermektedir.","Videoda, trigonometrik ifadeler içeren rasyonel fonksiyonların integralinde bu dönüşümün nasıl kolaylık sağladığını göstererek, karmaşık görünümlü integral problemlerinin nasıl basitleştirilebileceğini ve sonuca nasıl ulaşılabileceğini adım adım açıklamaktadır."]},"endTime":823,"title":"Yarım Açı Yöntemi ile Trigonometrik İntegral Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Yarım Açı Yöntemi Tanıtımı","list":{"type":"unordered","items":["Yarım açı yöntemi, tanjant x bölü iki eşittir t değişken dönüşümü yaparak trigonometrik ifadeler içeren rasyonel fonksiyonların integralini hesaplama yöntemidir.","Trigonometrik ifadeler temelde sinx ve cosx'tir ve integralde dx de vardır.","Tanjant x bölü iki t dönüşümü yapıldığında sinx, cosx ve dx'in t cinsinden karşılıkları 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yazılır.","Sekant integralinin sonucu ln|(1+t)/(1-t)| + C olarak bulunur, t yerine tanjant x bölü iki yazılır.","Kosekant integrali (1/sinx dx) için aynı dönüşüm uygulandığında integral ∫dt/t olarak yazılır ve sonucu ln|t| + C = ln|tanjant x bölü iki| + C olarak bulunur."]},"beginTime":196,"endTime":443,"href":"/video/preview/6686446158031290747?parent-reqid=1769720082062312-8160201163236053337-balancer-l7leveler-kubr-yp-klg-265-BAL&text=XTANIM+CREATION&t=196&ask_summarization=1"},{"index":3,"title":"Yarım Açı Formülü ile İntegral Çözümü","list":{"type":"unordered","items":["Trigonometrik ifadelerin rasyonel olduğu integral problemleri için yarım açı formülü kullanılabilir.","Tanjant x/2 = t dönüşümü yapılarak, cos x = (1-t²)/(1+t²), sin x = 2t/(1+t²) ve dx = 2dt/(1+t²) dönüşümleri uygulanır.","Karmaşık görünen integral, bu dönüşümlerle daha basit bir formuna 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