Question

integral of e^x+lnx^2dx

Answer 1

I mean \[\int\limits_{}^{} e^{x+lnx^2}dx\]

Answer 2

Integration by parts

Answer 3

u=x^2 dv=e^xdx
du=2xdx v=e^x
\[e^x x^2-2\int\limits e^x x \, dx \]

Answer 4

By parts again
u=x dv=e^x
du=dx v=e^x

Answer 5

\[e^x x^2-2 e^x x+2\int\limits e^x \, dx \]

Answer 6

Solve can simplify

Answer 7

I mean and*

Answer 8

how do we decide u and dv in general :(

Answer 9

Its integration by parts,
you must let u=x^2 NOT u=e^x because when you differentiate u=x^2, it will get smaller and smaller.

but if you take u=e^x then when you differentiate it it's still the same, and you'll get infinite loop