Lecture 3 Part 1 Integrals Class 12 Maths

Part - 1 Lecture - 3 Chapter 7 Integrals

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

बुज़दिल हैं वे लोग जो दूसरों के दम पर जिया करते हैं,
शेरदिल हैं वे लोग जो रास्तों के ग़म पर भी हस दिया करते हैं |

:::INTEGRATION BY PARTS:::

by parts

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Method to identify the First Function:

I    L    A    T    E

I = Inverse Trigonometric Functions
L = Logarithmic Functions
A = Algebraic Functions
T = Trigonometric Functions
E = Exponential functions

Questions Discussed in this lecture:

1. \int{xe^x}dx= xe^x-e^x+C

2. \int{x\cos{x}dx}= x\sin{x}+\cos{x}+C

3. \int{x\sin{3}x}dx=-\frac{x}{3}\cos{3}x+\frac{1}{9}\sin{3}x+C

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4. \int{x\log{2}x}dx=\frac{x^2}{2}\log{2}x-\frac{x^2}{4}+C

5. \int{x^5. \log{x}dx=}\frac{x^3}{3}\log{x}-\frac{x^3}{9}+C

6. \int{x{\tan}^{-1}{x}}dx=\frac{x^2}{2}{\tan}^{-1}{x}-\frac{x}{2}+\frac{1}{2}{\tan}^{-1}{x}+C

7. \int(x^2+1)\log{x}dx=\left(\frac{x^3}{3}+x\right)\log{x}-\frac{x^3}{9}-x+C

8. \int e^{2x}\sin{x}dx=\frac{e^{2x}}{5}(2\sin{x} – \cos{x})+C

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