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Mathematics
Mathematics
Problem
Find
∫
x
2
ln
x
d
x
\displaystyle \int x^{2}\,\ln x\,dx
∫
x
2
ln
x
d
x
. a)
x
3
2
ln
x
−
x
3
6
+
C
\dfrac{x^{3}}{2}\,\ln x-\dfrac{x^{3}}{6}+C
2
x
3
ln
x
−
6
x
3
+
C
b)
x
3
3
ln
x
+
x
3
9
+
C
\dfrac{x^{3}}{3}\,\ln x+\dfrac{x^{3}}{9}+C
3
x
3
ln
x
+
9
x
3
+
C
c)
x
3
3
ln
x
−
x
3
9
+
C
\dfrac{x^{3}}{3}\,\ln x-\dfrac{x^{3}}{9}+C
3
x
3
ln
x
−
9
x
3
+
C
d)
x
3
3
ln
x
+
C
\dfrac{x^{3}}{3}\,\ln x+C
3
x
3
ln
x
+
C
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