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
1. $\displaystyle \int\frac{x^2+x+1}{\sqrt(x)}dx=\int\frac{x^2}{\sqr t(x)}+\frac{x}{\sqrt(x)}+\frac{1}{\sqrt(x)}dx$
2.$\displaystyle \int\cot{x}dx=\ln{\sin(x)$ and $\displaystyle \int\csc{x}\cot{x}dx=-\csc{x}$
Read here first:
Exponentiation - Wikipedia, the free encyclopedia
then, here:
http://www.tech.plym.ac.uk/maths/res..._integrals.pdf
@Homeylova223:
It's really important you can work with powers and exponents etc ... so you have to know the basic rules, like: $\displaystyle a^{x}\cdot a^{y}=a^{x+y}$, etc...
Take a look at the site Also sprach Zarathrusta has given you.
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?
Because:
$\displaystyle \frac{x^2}{\sqrt{x}}$ $\displaystyle =\frac{x^2}{x^{\frac{1}{2}}}$ $\displaystyle =x^{2-\frac{1}{2}}=x^{\frac{3}{2}}$
This is what I meant with the fact you've to know the basic rules ...
EDIT:
Can you calculate the primitive function now?
You made a little mistake in the exponent of the second term, the primitive function has to be:
$\displaystyle F(x)=\frac{2}{5}\cdot x^{\frac{5}{2}}+\frac{2}{3}\cdot x^{\frac{3}{2}}+2\cdot x^{\frac{1}{2}}+C$