Evaluating indefinite integral thread number 1?

[homeylova223]

Can anyone help me integrate the following functions

1.((x^2+x+1))/((square root(x))

The square root on the denominator is confusing me.

2. ((1-csc(x) times cot(x))

Any help would be appreciated

[e^(i*pi)]

1. Use the fact that . This will give you three terms to integrate which can be done separately using the power rule

[waqarhaider]

1.

2. and

[homeylova223]

For my first question I have

((x^2))/square root(x)+(x)/square root(x)+1/square root(x)

Would anyone kindly help me integrate this.

[Also sprach Zarathustra]

For my first question I have

((x^2))/square root(x)+(x)/square root(x)+1/square root(x)

Would anyone kindly help me integrate this.

Read here first:

Exponentiation - Wikipedia, the free encyclopedia

then, here:

http://www.tech.plym.ac.uk/maths/res..._integrals.pdf

[waqarhaider]

now use power rule to integrate

[Siron]

@Homeylova223:
It's really important you can work with powers and exponents etc ... so you have to know the basic rules, like: , etc...
Take a look at the site Also sprach Zarathrusta has given you.

[homeylova223]

How do you know that ((x^2))/((square root(x))= x^(3/2)

Would you kindly show me? Because I have never done this type of intergral problem before and my textbook does not cover it.

I read the wiki but can anyone just help with this specific problem please.

Wait I think I understand do I use this rule (a^n)/(a^m)

a^n-a^m?

[Siron]

Because:


This is what I meant with the fact you've to know the basic rules ...

EDIT:
Can you calculate the primitive function now?

[homeylova223]

I think I can evaluate it I have

x^(3/2)+x^(1/2)+x^(-1/2)

(2/5)x^(5/2)+(2/3)x^(1/2)+2x^(1/2)?

[Siron]

You made a little mistake in the exponent of the second term, the primitive function has to be: