Some Complex Integrals

**phareouh** · February 24th 2010, 04:34 PM

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

**Prove It** · February 24th 2010, 08:06 PM

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. $\int{\frac{1}{\sec{x}}\,dx} = \int{\cos{x}\,dx}$ .

That's an easy one.

2. $\int{\frac{1}{1 + x^2}\,dx}$ .

For this one use a substitution $x = \tan{\theta}$ , making note that $dx = \sec^2{\theta}\,d\theta$ .

Also note that $\theta = \arctan{x}$ .

3. $\int{\tan{x}\,dx} = \int{\frac{\sin{x}}{\cos{x}}\,dx}$ .

Now use the substitution $u = \cos{x}$ .

4. $\int{\cot{x}\,dx} = \int{\frac{\cos{x}}{\sin{x}}\,dx}$ .

Now use the substitution $u = \sin{x}$ .

5. I can't tell if that's $\int{\frac{1}{2x}\,dx}$ or $\int{\frac{1}{2}x\,dx}$ .

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