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Mathematics
Mathematics
Problem
Determine
∫
x
2
(
ln
x
)
2
d
x
\displaystyle \int x^{2}\,(\ln x)^{2}\,dx
∫
x
2
(
ln
x
)
2
d
x
. a)
x
3
(
(
ln
x
)
2
3
+
2
ln
x
9
−
2
27
)
+
C
x^{3}\Bigl(\dfrac{(\ln x)^{2}}{3}+\dfrac{2\,\ln x}{9}-\dfrac{2}{27}\Bigr)+C
x
3
(
3
(
ln
x
)
2
+
9
2
ln
x
−
27
2
)
+
C
b)
x
3
3
(
ln
x
)
2
−
2
x
3
ln
x
3
+
C
\dfrac{x^{3}}{3}(\ln x)^{2}-\dfrac{2x^{3}\ln x}{3}+C
3
x
3
(
ln
x
)
2
−
3
2
x
3
ln
x
+
C
c)
x
3
(
(
ln
x
)
2
3
−
2
ln
x
9
+
2
27
)
+
C
x^{3}\Bigl(\dfrac{(\ln x)^{2}}{3}-\dfrac{2\,\ln x}{9}+\dfrac{2}{27}\Bigr)+C
x
3
(
3
(
ln
x
)
2
−
9
2
ln
x
+
27
2
)
+
C
d)
x
3
(
(
ln
x
)
2
3
−
2
ln
x
9
+
1
27
)
+
C
x^{3}\Bigl(\dfrac{(\ln x)^{2}}{3}-\dfrac{2\,\ln x}{9}+\dfrac{1}{27}\Bigr)+C
x
3
(
3
(
ln
x
)
2
−
9
2
ln
x
+
27
1
)
+
C
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