1. Some Complex Integrals

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

2. Originally Posted by phareouh
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 $\displaystyle \int{\frac{1}{2}x\,dx}$.