# 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 **