Hi guys , i want you to help me to figure out some Complex integral forms , that need to be memorized thank you :
Int 1/(sec x)
int 1/(1+x^2)
int tan x
int cot x
int 1/2x
and a quick note on int of exponential functions ,
thanks
1. $\displaystyle \int{\frac{1}{\sec{x}}\,dx} = \int{\cos{x}\,dx}$.
That's an easy one.
2. $\displaystyle \int{\frac{1}{1 + x^2}\,dx}$.
For this one use a substitution $\displaystyle x = \tan{\theta}$, making note that $\displaystyle dx = \sec^2{\theta}\,d\theta$.
Also note that $\displaystyle \theta = \arctan{x}$.
3. $\displaystyle \int{\tan{x}\,dx} = \int{\frac{\sin{x}}{\cos{x}}\,dx}$.
Now use the substitution $\displaystyle u = \cos{x}$.
4. $\displaystyle \int{\cot{x}\,dx} = \int{\frac{\cos{x}}{\sin{x}}\,dx}$.
Now use the substitution $\displaystyle u = \sin{x}$.
5. I can't tell if that's $\displaystyle \int{\frac{1}{2x}\,dx}$ or $\displaystyle \int{\frac{1}{2}x\,dx}$.