Calculus 2 Quiz
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TECHNIQUES OF INTEGRATION
Question 1
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Evaluate
∫
x
arcsin
(
x
)
d
x
\int x \arcsin(x) \,dx
∫
x
arcsin
(
x
)
d
x
.
A
x
2
2
arcsin
(
x
)
−
1
4
x
1
−
x
2
+
1
4
arcsin
(
x
)
+
C
\frac{x^2}{2}\arcsin(x) - \frac{1}{4}x\sqrt{1-x^2} + \frac{1}{4}\arcsin(x) + C
2
x
2
arcsin
(
x
)
−
4
1
x
1
−
x
2
+
4
1
arcsin
(
x
)
+
C
B
x
2
2
arcsin
(
x
)
+
1
2
x
1
−
x
2
−
1
2
arcsin
(
x
)
+
C
\frac{x^2}{2}\arcsin(x) + \frac{1}{2}x\sqrt{1-x^2} - \frac{1}{2}\arcsin(x) + C
2
x
2
arcsin
(
x
)
+
2
1
x
1
−
x
2
−
2
1
arcsin
(
x
)
+
C
C
x
2
arcsin
(
x
)
−
1
4
x
1
−
x
2
+
C
x^2\arcsin(x) - \frac{1}{4}x\sqrt{1-x^2} + C
x
2
arcsin
(
x
)
−
4
1
x
1
−
x
2
+
C
D
x
2
2
arcsin
(
x
)
+
1
4
x
1
−
x
2
−
1
4
arcsin
(
x
)
+
C
\frac{x^2}{2}\arcsin(x) + \frac{1}{4}x\sqrt{1-x^2} - \frac{1}{4}\arcsin(x) + C
2
x
2
arcsin
(
x
)
+
4
1
x
1
−
x
2
−
4
1
arcsin
(
x
)
+
C
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