1. ## hard integration problem

problem is integrate (5^x + 2e^5lnx) dx

I can only think to take the natural log of both sides :

xln5 + (5lnx)(ln2e)

so then I try to integrate by parts for xln5 and get :
xln5 = (ln5(x^2))/2 - (ln5(x^2))/2 + xln5 OR 0=0.

So integration by parts for xln5 wont work

So next thing and last thing I can think of is to combine ln5^x +ln2e^5lnx =
integral of ln[(5^x)(2e^5lnx)]

But how do I do this? no clue.

2. Is it 2e^(5lnx)?

3. Originally Posted by frankinaround
problem is integrate (5^x + 2e^5lnx) dx

I can only think to take the natural log of both sides :

xln5 + (5lnx)(ln2e)

so then I try to integrate by parts for xln5 and get :
xln5 = (ln5(x^2))/2 - (ln5(x^2))/2 + xln5 OR 0=0.

So integration by parts for xln5 wont work

So next thing and last thing I can think of is to combine ln5^x +ln2e^5lnx =
integral of ln[(5^x)(2e^5lnx)]

But how do I do this? no clue.
e^{5 \ln x} = e^{\ln x^5} = x^5

5^x = e^{kx} where k = \ln (5).

You should know how to integrate both of the above.

4. Originally Posted by mr fantastic
e^{5 \ln x} = e^{\ln x^5} = x^5

5^x = e^{kx} where k = \ln (5).

You should know how to integrate both of the above.
wow wow yeah I get it. 2e^5lnx = 2x^5 right, but 5^x I dont follow AS well, can you elaborate on that just a LITTLE bit?

5. integral of a^x is (a^x)/(ln a) + C

6. Originally Posted by frankinaround
wow wow yeah I get it. 2e^5lnx = 2x^5 right, but 5^x I dont follow AS well, can you elaborate on that just a LITTLE bit?
Let y = 5^x.

Then ln(y) = x ln(5).

Exponentiate both sides to base e:

y = 5^x = e^{x ln(5)}.