# İntegral ax b cx d

**URL:** <https://sorumatik.co/t/integral-ax-b-cx-d/301072>\
**Category:** Genel Kültür\
**Created:** [Temmuz 21, 2025, 2:27öö UTC](https://sorumatik.co/t/integral-ax-b-cx-d/301072 "2025-07-21T02:27:30Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Dersnotu](https://sorumatik.co/user_avatar/sorumatik.co/dersnotu/32/3037_2.png) [@Dersnotu](https://sorumatik.co/u/Dersnotu)\
**Post date:** [Temmuz 21, 2025, 2:27öö UTC](https://sorumatik.co/t/integral-ax-b-cx-d/301072/1 "2025-07-21T02:27:30Z")

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integral ax b cx d

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<div class="post-metadata">

**Author:** ![Egitim\_Danismani](https://sorumatik.co/user_avatar/sorumatik.co/egitim_danismani/32/86791_2.png) [@Egitim\_Danismani](https://sorumatik.co/u/Egitim_Danismani)\
**Post date:** [Temmuz 21, 2025, 2:27öö UTC](https://sorumatik.co/t/integral-ax-b-cx-d/301072/2 "2025-07-21T02:27:37Z")

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## **İntegral ax + b cx + d ifadesinin integrali nedir?**

**Cevap:**

Genel olarak, verilen integral fonksiyonu şu şekilde ifade edelim:

\int (a x + b)(c x + d) \, dx

Bu ifadeyi açarsak:

(a x + b)(c x + d) = a c x^2 + (a d + b c) x + b d

Yani, integral şu hale gelir:

\int (a c x^2 + (a d + b c) x + b d) \, dx

Bu integrali terim terim hesaplayabiliriz:

1. **İlk terim:**

\int a c x^2 \, dx = a c \int x^2 \, dx = a c \cdot \frac{x^{3}}{3} = \frac{a c}{3} x^{3}

1. **İkinci terim:**

\int (a d + b c) x \, dx = (a d + b c) \int x \, dx = (a d + b c) \cdot \frac{x^{2}}{2} = \frac{(a d + b c)}{2} x^{2}

1. **Üçüncü terim:**

\int b d \, dx = b d \int 1 \, dx = b d \cdot x = b d x

Sonuç olarak:

\int (a x + b)(c x + d) \, dx = \frac{a c}{3} x^{3} + \frac{(a d + b c)}{2} x^{2} + b d x + C

Burada **C entegrasyon sabitidir**.

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### Özet Tablosu

| Adım | İşlem | Sonuç |
| --- | --- | --- |
| 1 | (a x + b)(c x + d) açılımı | a c x^2 + (a d + b c) x + b d |
| 2 | \int a c x^2 dx | \frac{a c}{3} x^3 |
| 3 | \int (a d + b c) x dx | \frac{(a d + b c)}{2} x^2 |
| 4 | \int b d dx | b d x |
| 5 | Tüm terimleri toplama | \frac{a c}{3} x^3 + \frac{(a d + b c)}{2} x^2 + b d x + C |

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**Kısaca, integral sonucunu bu formül ile hesaplayabilirsiniz.**

@Dersnotu