# Lecture 3 Part 3 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 - 2

There’s a special case $\int{e^x(f(x)+f^\prime(x))=e^xf(x)+C}$. You may need a little bit of simplification to apply this identity:

12. $\int{e^x(\sin{x}+\cos{x})dx= e^x\sin{x}}+C$

13. $\int\frac{xe^x}{(1+x)^2}dx=\frac{e^x}{1+x}+C$

14. $\int\frac{(x-4)e^x}{(x-2)^3}dx=\frac{e^x}{(x-2)^2}+C$

15. $\int\frac{2+\sin{2}x}{1+\cos{2}x}e^xdx=\ e^x\tan{x}+C$

16. $\int{e^x\left(\frac{\sin{4}x-4}{1-\cos{4}x}\right)}dx=\ e^x.\cot{2}x+C$

17. $\int\frac{(x^2+1)e^x}{(x+1)^2}dx=\left(\frac{x-1}{x+1}\right)e^x+C$

18. $\int{e^x\left(\frac{1-x}{1+x^2}\right)^2dx=\frac{e^x}{1+x^2}}+C$

19. $\int_{\frac{\pi}{2}}^{\pi}{e^x\left(\frac{1-\sin{x}}{1-\cos{x}}\right)}dx=\ e^\frac{\pi}{2}$