Lecture 8 | ⭐ Indefinite Integration By Parts ⭐ | Class 12th | Forms 18,19, 20 & 21

This lecture includes Discussion of the concept of Integral Calculus. This is lecture-8 on Indefinite Integration and it covers integration of functions
⭐ By Parts ⭐. It covers forms 18,19, 20 & 21 of indefinite integration.

This Lecture Covers, concept, which have been detailed with timeline in the Description below:

The Lecture is taken by Abhishek Jaiswal (B.TECH IIT Roorkee). For queries call 9312922770.

This lecture includes following topic with timelines (hh:mm:ss):

1. Indefinite Integration | Form-18 | Integration By Parts | Introduction | (00:03:13)

🔥Suggestive order of functions for applying By Parts | ILATE | (00:13:25)

Example 1 | ∫ x eˣ dx | (00:19:58)

Example 2 | ∫ x² cos x dx | (00:22:05)

Example 3 | ∫ tanˉ¹x dx | (00:24:25)

Example 4 | ∫ ln x dx | (00:29:24)

Example 5 | ∫ e^(√x) dx | (00:32:41)

Example 6 | ∫ x³ sinˉ¹(x²)/(√1 - x⁴) dx | (00:36:16)

🔥 Example 7 | ∫ (sinˉ¹(√x - cosˉ¹(√x)/ (sinˉ¹(√x + cosˉ¹(√x) dx | (00:42:00)

2. Indefinite Integration | Form-19 | Integration By Parts involving cancellation | ∫ eˣ [ f(x) + f ՜(x)] dx = eˣ f(x) + C | (00:52:00)

Example 1 | ∫ eˣ ( sin x + cos x )dx | (00:58:24)

Example 2 | ∫ eˣ ( 1/x – 1/x² )dx | (01:00:40)

Example 3 | ∫ xeˣ/( x + 1)² dx | (01:02:08)

Example 4 | ∫ eˣ (ln x + 1/x)dx | (01:04:37)

🔥Example 5 | ∫ eˣ [ ln(secx + tanx) + secx] dx | (01:06:28)

Example 6 | ∫ eˣ (2 + sin 2x)/(1 + cos 2x) dx | (01:10:28)

🔥Example 7 | ∫ [ln(ln x) + 1/ (ln x)²] dx | (01:12:52)

3. Indefinite Integration | Form-20 | Integration By Parts involving LOOP |
∫ e ͣ ˣ Sin bx dx | ∫ e ͣ ˣ Cos bx dx | (01:23:32)

Example 1 | ∫ e⁴ˣcos3x dx | (01:38:22)

Example 2 | ∫ eˣcos²x dx | (01:40:14)

🔥Example 3 | ∫ Sin(lnx) dx | (01:42:54)

🔥 Euler Proof of above outcomes ∫ e ͣ ˣ Sin bx dx | ∫ e ͣ ˣ Cos bx dx | (01:46:20)

4. Indefinite Integration | Form-21 | 3 more formulas | ∫ √quadratix dx |
∫ √(x² - a²) dx | ∫ √(x² + a²) dx | ∫ √(a² - x²) dx | (01:54:39)

Example 1 | ∫ √(4 - x²) dx | (02:06:56)

Example 2 | ∫ √(1 - 9x²) dx | (02:08:09)

Example 3 | √(x² + 2x + 3) dx | (02:11:20)

🔥Example 4 | (2x + 1)√(x² + 2x + 2) dx | (02:13:10)

5. Miscellaneous Example | 🔥 ∫ x²/(x sinx + cosx)² dx | (02:19:26)

#IndefiniteIntegration #GetTrainedByIITians #IITMaths

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[karansoam]

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Loved being taught by you at greycellls sir.