∫
(
e
2
ln
x
+
e
2
x
)
d
x
=
\displaystyle \int (e^{2\ln x}+e^{2x}) dx =
∫
(
e
2
l
n
x
+
e
2
x
)
d
x
=
2
+
e
2
x
2
+
C
2+\dfrac{e^{2x}}{2}+C
2
+
2
e
2
x
+
C
e
x
3
3
+
2
e
2
x
+
C
\dfrac{e^{x^3}}{3}+2e^{2x}+C
3
e
x
3
+
2
e
2
x
+
C
e
x
3
3
+
e
2
x
2
+
C
\dfrac{e^{x^3}}{3}+\dfrac{e^{2x}}{2}+C
3
e
x
3
+
2
e
2
x
+
C
x
3
3
+
e
2
x
2
+
C
\dfrac{x^3}{3}+\dfrac{e^{2x}}{2}+C
3
x
3
+
2
e
2
x
+
C
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Approach
∫
(
e
2
ln
x
+
e
2
x
)
d
x
=
∫
(
e
ln
x
2
+
e
2
x
)
d
x
\int (e^{2\ln x}+e^{2x}) dx = \int (e^{\ln x^2}+e^{2x}) dx
∫
(
e
2
l
n
x
+
e
2
x
)
d
x
=
∫
(
e
l
n
x
2
+
e
2
x
)
d
x
=
∫
(
x
2
+
e
2
x
)
d
x
= \int (x^2+e^{2x}) dx
=
∫
(
x
2
+
e
2
x
)
d
x
=
x
3
3
+
e
2
x
2
+
C
= \boxed{\frac{x^3}{3} + \frac{e^{2x}}{2} + C}
=
3
x
3
+
2
e
2
x
+
C