# Lecture 3 Part 1 Integrals Class 12 Maths :::INTEGRATION BY PARTS:::

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

## VIDEO - 1 CLIP - 2

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