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