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Mathematics
Mathematics
Problem
Find an antiderivative of
∫
x
ln
(
x
2
)
d
x
\displaystyle \int x\,\ln\bigl(x^{2}\bigr)\,dx
∫
x
ln
(
x
2
)
d
x
. a)
x
ln
(
x
2
)
−
x
+
C
x\ln\bigl(x^{2}\bigr)-x+C
x
ln
(
x
2
)
−
x
+
C
b)
x
2
ln
(
x
2
)
−
x
2
2
+
C
\dfrac{x^{2}\ln\bigl(x^{2}\bigr)-x^{2}}{2}+C
2
x
2
ln
(
x
2
)
−
x
2
+
C
c)
x
2
ln
(
x
2
)
+
x
2
2
+
C
\dfrac{x^{2}\ln\bigl(x^{2}\bigr)+x^{2}}{2}+C
2
x
2
ln
(
x
2
)
+
x
2
+
C
d)
x
2
ln
(
x
2
)
−
x
2
+
C
x^{2}\ln\bigl(x^{2}\bigr)-x^{2}+C
x
2
ln
(
x
2
)
−
x
2
+
C
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