Question

How to integrate:
\(\Huge \int x(2^x) dx\)?

Answer 1

by parts\[dv=2^xdx\]\[u=x\]

Answer 2

errrr..... how to integrate the 2^x?
I know this can be done by part but i duno how to integrate 2^x...

Answer 3

Are you still viewing this problem?

Answer 4

The integral of 2^x is 2^x/ln2

Answer 5

why and how......

Answer 6

\[\int\limits\limits_{}^{}a^xdx=\int\limits\limits_{}^{}e^{\ln(a^x)}dx=\int\limits_{}^{}e^{xln(a)}dx=\frac{e^{xln(a)}}{\ln(a)}=\frac{a^x}{\ln(a)}\]

Answer 7

You need to go back to logarithmic differentiate to understand that one :)
\[y=a^x\]\[\ln y=x \ln a\]\[\frac{ y' }{ y }=\ln a\]\[y'=y \ln a = a^x \ln a\]

So think about this a second, if you take the derivative of this function what do you get:\[y=\frac{ 1 }{ \ln a }a^x\]\[y'=(\frac{ 1 }{ \ln a })a^x \ln a = a^x\]

Or writing it the way ivan did works really nicely too ^^
I like that better actually, heh.

Answer 8

oh thanks for explaining!