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Mathematics
Problem
Consider the integral
∫
x
−
4
e
x
−
3
d
x
\displaystyle\int x^{-4} e^{x^{-3}}\,dx
∫
x
−
4
e
x
−
3
d
x
. After the substitution
u
=
x
−
3
u = x^{-3}
u
=
x
−
3
, which of the following integrals is obtained? a)
∫
3
e
u
d
u
\displaystyle\int 3e^{u}\,du
∫
3
e
u
d
u
b)
∫
e
u
d
u
\displaystyle\int e^{u}\,du
∫
e
u
d
u
c)
∫
−
1
3
e
u
d
u
\displaystyle\int -\tfrac{1}{3}e^{u}\,du
∫
−
3
1
e
u
d
u
d)
∫
−
e
u
d
u
\displaystyle\int -e^{u}\,du
∫
−
e
u
d
u
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