# Thread: Integrating different kinds of functions

1. ## Integrating different kinds of functions

I have an assignment, which is to show the proofs for

$\displaystyle f(x)=x^{n}$
$\displaystyle F(x)=\frac{x^{n+1}}{n+1}+k$

And also proofs for how you integrate logarithm functions:
$\displaystyle log(x), ln(x)$

And trigonometric functions:
$\displaystyle sin(x), cos(x), tan(x)$

I looked in my books, but they don't have any proofs for why you get what you get when integrating them.

2. Originally Posted by No Logic Sense
I have an assignment, which is to show the proofs for

$\displaystyle f(x)=x^{n}$
$\displaystyle F(x)=\frac{x^{n+1}}{n+1}+k$
$\displaystyle \int{x^{n}\,dx}=\int{e^{n\ln x}\,dx}.$ Now put $\displaystyle u=\ln x$ and the integral becomes $\displaystyle \int e^{(n+1)u}\,du=\frac{e^{(n+1)\ln x}}{n+1}+k=\frac{x^{n+1}}{n+1}+k.$

3. I'm sorry, but I don't quite understand how you got the natural constant (e) (I'm not sure if that is what it's called in English) or how you got the +1 later on.