<s>[INST] Evaluate the Integral: $\int(x^5+5^x)\ dx$ $\int(x^5+5^x)\ dx$
I made the the terms within the parenthesis u
$u=x^5+5^x$
$du=5x^4+5^xln\ 5$ 
$du=5x^4+5^x\ ln\ 5 dx$
$\frac{u}{5x^4+5^xln\ 5}\ du$
I am stuck at this point. Is there a better way to attack this problem? I know I have to use this formula 

$\int\ a^x dx=\frac{a^x}{ln\ a}+C$

But how? 
 [/INST] If you want to evaluate this integral, you should simplify like this:
$\int{(x^5 + 5^x) dx} = \int{x^5 dx} + \int{5^x dx}$. You can always split up an expression of the same variable like this to simplify your computation. Now, generally, $\int{x^ndx} = \frac{x^{n+1}}{n+1} +C$, and $\int{a^xdx} = \frac{a^x}{ln{(a)}} +C$.
So, our result is: $\int{x^5 dx} + \int{5^x dx} = \frac{x^6}{6} + \frac{5^x}{ln{(5)}} +C$. $C$ is the constant of integration, due to the integral being indefinite.
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