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Mathematics
Problem
Evaluate
∫
5
e
5
x
−
4
e
4
x
e
5
x
−
e
4
x
d
x
\displaystyle \int \frac{5e^{5x}-4e^{4x}}{e^{5x}-e^{4x}}\,dx
∫
e
5
x
−
e
4
x
5
e
5
x
−
4
e
4
x
d
x
. a)
ln
∣
e
5
x
+
e
4
x
∣
+
C
\ln|e^{5x}+e^{4x}|+C
ln
∣
e
5
x
+
e
4
x
∣
+
C
b)
ln
∣
e
5
x
−
e
4
x
∣
+
C
\ln|e^{5x}-e^{4x}|+C
ln
∣
e
5
x
−
e
4
x
∣
+
C
c)
ln
∣
5
e
5
x
−
4
e
4
x
∣
+
C
\ln|5e^{5x}-4e^{4x}|+C
ln
∣5
e
5
x
−
4
e
4
x
∣
+
C
d)
e
5
x
−
e
4
x
+
C
e^{5x}-e^{4x}+C
e
5
x
−
e
4
x
+
C
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