Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A student rewrites the integral
∫
x
3
e
x
2
d
x
\displaystyle \int x^{3} e^{x^{2}}\,dx
∫
x
3
e
x
2
d
x
by substituting
u
=
x
2
u = x^{2}
u
=
x
2
, obtaining
1
2
∫
u
e
u
d
u
\frac12\int u e^{u}\,du
2
1
∫
u
e
u
d
u
. In one concise sentence, explain why the integral
∫
u
e
u
d
u
\int u e^{u}\,du
∫
u
e
u
d
u
is not immediately solvable by consulting a standard table of basic antiderivatives.
Browse the problem library