Question

I need help with the integral of

x^2x(1+lnx)dx , x from 2 to 4.

Thanks for any help!

Answer 1

i have no idea, but i would first turn it in to
\[\int e^{2x\ln(x)}(1+\ln(x))dx\]

Answer 2

It looks complicated, but it's not that
\[\int_2^4 x^{2x}(1+lnx)dx\]
Let \(u= x^{2x}\) --> \(ln u = ln x^{2x}= 2xlnx\)
take derivative respect to x
\(\dfrac{u'}{u}= 2(lnx+1)dx\) --> du = \(2x^{2x}(lnx+1)dx\) --> \(\dfrac{du}{2}= 2^{2x}(lnx+1) dx\)
your duty is change the limit and solve, so simple, right?

Answer 3

Thanks, Loser66!

Answer 4

np