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Teoremas de integracion directa
This document outlines 15 integration theorems with examples, including: 1) Integrating a with respect to x equals ax + c 2) Integrating sec^2(x) with respect to x equals tan(x) + c 3) Integrating csc^2(x) with respect to x equals -cot(x) + c
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Teoremas de integracion directa
- 1.
- 2. 𝑎𝑑𝑥 = 𝑎𝑑𝑥 = 𝑎𝑥 + 𝑐 • EJEMPLO 5𝑑𝑥 = 5 𝑑𝑥 = 5𝑥 + 𝑐
- 3.
- 4.
- 9. TEOREMA 8 • 𝒔𝒆𝒄𝟐 𝒙𝒅𝒙 = 𝐭𝐚𝐧 𝒙 + 𝒄 EJEMPLO 𝟏𝟖𝒔𝒆𝒄 𝟐 𝒙𝒅𝒙 = 𝟏𝟖 𝒔𝒆𝒄 𝟐 𝒙𝒅𝒙 19 tan x +𝒄
- 10. TEOREMA 9 • 𝒄𝒔𝒄𝟐 𝒙𝒅𝒙 = − 𝐜𝐨𝐭 𝒙 + 𝒄 EJEMPLO • 𝟏𝟒 𝒄𝒔𝒄 𝟐 x dx = 14 𝒄𝒔𝒄 𝟐 𝒙 𝒅𝒙 14 cot x +𝒄
- 11. TEOREMA 10 • 𝐬𝐞𝐜𝒙 ∙ 𝐭𝐚𝐧 𝒙 𝒅𝒙 = 𝐬𝐞𝐜 𝒙 + 𝒄 EJEMPLO 𝐬𝐞𝐜 𝒙 ∙ 𝐭𝐚𝐧 𝒙 𝒅𝒙 = 𝐬𝐞𝐜 𝒙 + 𝒄
- 12. TEOREMA 11 • 𝐜𝐬𝐜𝒙 ∙ 𝐜𝐨𝐭 𝒙 𝒅𝒙 = − 𝐜𝐬𝐜 𝒙 + 𝒄 EJEMPLO 𝐜𝐬𝐜 𝒙 ∙ 𝐜𝐨𝐭 𝒙 𝒅𝒙 = − 𝐜𝐬𝐜 𝒙 + 𝒄
- 13. TEOREMA 12 • 𝒂𝒓𝒄𝐭𝐚𝐧 𝒖 𝒅𝒖 = 𝟏 𝟏+𝒖 𝟐 + 𝒄 EJEMPLO 𝒂𝒓𝒄 𝐭𝐚𝐧 𝟓 𝒅𝒖 = 𝟏 𝟏+𝟓 𝟐 + 𝒄
- 14. TEOREMA 13 • 𝒂𝒓𝒄𝐬𝐢𝐧 𝒖 𝒅𝒖 = 𝟏 𝟏+𝒙 𝟐 +𝒄 EJEMPLO 𝒂𝒓𝒄 𝐬𝐢𝐧 𝟔 𝒅𝒖 = 𝟏 𝟏+𝟔 𝟐 +𝒄
- 15. TEOREMA 14 • 𝒂𝒓𝒄𝐜𝐨𝐬 𝒖 𝒅𝒖 = − 𝟏 𝟏+𝒙 𝟐 +𝒄 EJEMPLO 𝒂𝒓𝒄 𝐜𝐨𝐬 𝟕 𝒅𝒖 = − 𝟏 𝟏+𝟕 𝟐 +𝒄
- 16. TEOREMA 15 • 𝑑𝑥 𝑎2 +𝑢2 = 1 𝑎 arc tan 𝑢 𝑎 + 𝑐 EJEMPLO 𝑑𝑥 32 + 42 = 1 3 arc tan 𝑢 4 +𝑐