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Mathematics
Mathematics
Problem
Prove that for non-zero constants
a
a
a
and
b
b
b
,
∫
e
a
x
sin
b
x
d
x
=
e
a
x
(
a
sin
b
x
−
b
cos
b
x
)
a
2
+
b
2
+
C
.
\int e^{ax}\sin bx\,dx=\frac{e^{ax}(a\sin bx-b\cos bx)}{a^{2}+b^{2}}+C.
∫
e
a
x
sin
b
x
d
x
=
a
2
+
b
2
e
a
x
(
a
sin
b
x
−
b
cos
b
x
)
+
C
.
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