Part II: The Answers
370
Answers
501–600
591.
–csc x + C
Rewrite the integrand. Then use trigonometric identities followed by using a basic antiderivative formula:
cos
sin
cos
sin
sin
cot csc
csc
x
x
dx
x
x
x
dx
x
xdx
x C
2
1
∫
∫
∫
=
( )
=
= −
+
592.
− +
+
1 5
4
4
x
x C
Begin by splitting up the fraction and simplifying the integrand:
x
x
x
dx
x
x
x
x
dx
x
x dx
+
=
+






=
+
(
)
∫
∫
∫
−
5
5
5
6
3
3
6
3
2
3
Then use elementary antiderivative formulas:
x
x dx x
x
C
x
x C
−
−
+
(
) = −
+
+
= − +
+
∫
2
3
1
4
4
5
1
5 4
1 5
4
593.
7
13
7
6
13 7
67
x
x
C
+
+
Begin by splitting up the fraction and simplifying the integrand:
x
x
dx
x
x
x
dx
x
x
dx
+
=
+




=
+
(
)
∫
∫
∫
−
1
1
7
1 7
1 7
6 7
1 7
Then use elementary antiderivative formulas:
x
x
dx x
x
C
x
x
C
6 7
1 7
13 7
67
13 7
67
13 7
6 7
7
13
7
6
+
(
) =
+
+
=
+
+
−
∫
594.
–cot x + x + C
Begin by splitting up the fraction and using trigonometric identities to rewrite the
integrand:
1
1
1
2
2
2
2
2
2
+
=
+






=
+
(
)
∫
∫
∫
sin
sin
s in
sin
sin
csc
x
x
dx
x
x
x
dx
x
dx