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Mathematics
Mathematics
Problem
Show that
∫
(
a
x
+
b
)
e
k
x
d
x
=
e
k
x
(
a
x
+
b
k
−
a
k
2
)
+
C
\displaystyle \int (ax + b)e^{kx}\,dx = e^{kx}\left(\dfrac{ax + b}{k} - \dfrac{a}{k^{2}}\right)+C
∫
(
a
x
+
b
)
e
k
x
d
x
=
e
k
x
(
k
a
x
+
b
−
k
2
a
)
+
C
, where
a
a
a
,
b
b
b
, and
k
k
k
are constants and
k
≠
0
k\neq 0
k
=
0
.
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