371
Answers
501–600
Answers and Explanations
Now apply elementary antiderivative formulas:
csc
cot
2
1
x
dx
x x C
+
(
)
= −
+ +
∫
595.
2
2
3
2
3
x x
x
C
−
−
+
Multiply out the integrand and then use elementary antiderivative formulas on each
term:
(
)(
)
1
2
2
2
2
3
2
2
3
−
+
=
− −
(
)
=
−
−
+
∫
∫
x
x dx
x x dx
x x
x
C
596.
tan x – x + C
Begin by multiplying out the integrand. Then simplify and use elementary antiderivative formulas:
sec (sec
cos )
s ec
sec cos
sec
cos
cos
x
x
x dx
x
x
x dx
x
x
x dx
−
=
−
(
)
=
−
(
)
∫
∫
2
2
1
∫ ∫
∫
=
−
(
)
=
− +
sec
tan
2
1
x
dx
x x C
597.
x
x C
2
2
3
−
+
Factor the numerator out of the integrand. Then simplify and use elementary antiderivative formulas:
x
x
x
dx
x
x
x
dx
x
dx
x
x C
2
2
5
6
2
2
3
2
3
2
3
−
+
−
=
−
−
−
=
−
=
−
+
∫
∫
∫
(
)(
)
(
)
(
)
598.
x
x
x C
3
2
3
2
−
+ +
Begin by factoring the numerator. Then simplify and use elementary antiderivative
formulas:
x
x
dx
x
x x
x
dx
x x
dx
x
x
x C
3
2
2
3
2
1
1
1
1
1
1
3
2
+
+
=
+
− +
(
)
+
=
− +
(
)
=
−
+ +
∫
∫
∫
(
)
(
)