Question

integrate the following function with respect to x:

e^xloga e^x​

Answer 1

Answer:

e^xlogae^x

=(e^x)^2loga

=e^2x(loga)

integration(e^2x(loga))=?

Let e^x=t=>e^2x=t^2

2e^2xdx=2tdt=>dx=t/t^2=1/t

integration((e^2x(loga))dx

=integration ((t^2(loga))dx)

=integration((t^2(loga))(1/t)dt)

=loga.integration(tdt)

=loga(t^2/2)

=loga(e^2x/2)

(since,e^2x=t^2)