1. ## Evaluating indefinite integral thread number 1?

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

2. ## Re: Evaluating indefinite integral thread number 1?

1. Use the fact that $\dfrac{a+b+c}{d} = \dfrac{a}{d} + \dfrac{b}{d} +\dfrac{c}{d}$. This will give you three terms to integrate which can be done separately using the power rule

3. ## Re: Evaluating indefinite integral thread number 1?

1. $\int\frac{x^2+x+1}{\sqrt(x)}dx=\int\frac{x^2}{\sqr t(x)}+\frac{x}{\sqrt(x)}+\frac{1}{\sqrt(x)}dx$

2. $\int\cot{x}dx=\ln{\sin(x)$ and $\int\csc{x}\cot{x}dx=-\csc{x}$

4. ## Re: Evaluating indefinite integral thread number 1?

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.

5. ## Re: Evaluating indefinite integral thread number 1?

Originally Posted by 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.

Exponentiation - Wikipedia, the free encyclopedia

then, here:

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

6. ## Re: Evaluating indefinite integral thread number 1?

$\frac{x^2}{\sqrt(x)}=x^\frac{3}{2}$ now use power rule to integrate

7. ## Re: Evaluating indefinite integral thread number 1?

@Homeylova223:
It's really important you can work with powers and exponents etc ... so you have to know the basic rules, like: $a^{x}\cdot a^{y}=a^{x+y}$, etc...
Take a look at the site Also sprach Zarathrusta has given you.

8. ## Re: Evaluating indefinite integral thread number 1?

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?

9. ## Re: Evaluating indefinite integral thread number 1?

Because:
$\frac{x^2}{\sqrt{x}}$ $=\frac{x^2}{x^{\frac{1}{2}}}$ $=x^{2-\frac{1}{2}}=x^{\frac{3}{2}}$

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

EDIT:
Can you calculate the primitive function now?

10. ## Re: Evaluating indefinite integral thread number 1?

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)?

11. ## Re: Evaluating indefinite integral thread number 1?

You made a little mistake in the exponent of the second term, the primitive function has to be:
$F(x)=\frac{2}{5}\cdot x^{\frac{5}{2}}+\frac{2}{3}\cdot x^{\frac{3}{2}}+2\cdot x^{\frac{1}{2}}+C$