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Mathematics
Mathematics
Problem
Find the indefinite integral
∫
x
ln
x
d
x
\displaystyle \int x\,\ln x\,dx
∫
x
ln
x
d
x
. a)
x
2
2
ln
x
+
x
2
4
+
C
\dfrac{x^{2}}{2}\,\ln x + \dfrac{x^{2}}{4} + C
2
x
2
ln
x
+
4
x
2
+
C
b)
x
2
2
ln
x
−
x
2
2
+
C
\dfrac{x^{2}}{2}\,\ln x - \dfrac{x^{2}}{2} + C
2
x
2
ln
x
−
2
x
2
+
C
c)
x
2
2
ln
x
−
x
2
4
+
C
\dfrac{x^{2}}{2}\,\ln x - \dfrac{x^{2}}{4} + C
2
x
2
ln
x
−
4
x
2
+
C
d)
x
2
4
ln
x
−
x
2
2
+
C
\dfrac{x^{2}}{4}\,\ln x - \dfrac{x^{2}}{2} + C
4
x
2
ln
x
−
2
x
2
+
C
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