Part II: The Answers
372
Answers
601–700
599.
20
13
5
19
2 6
3 8
x
x
C
.
.
−
+
When finding the antiderivative, don’t be thrown off by the decimal exponents; simply
add 1 to the exponent of each term and divide by that new exponent for each term to
get the solution:
4
4 2 6
3 8
4 26 10
38 10
20
1 6
2 8
2 6
3 8
2 6
3 8
x
x
dx
x
x
C
x
x
C
.
.
.
.
.
.
.
.
−
(
) =
−
+
=
−
+
=
∫
1 13
5
19
2 6
3 8
x
x
C
.
.
−
+
600.
−
−
+
50
11
10
1 1
0 1
x
x
C
.
.
Begin by splitting up the fraction and simplifying:
5
5
5
2 1
2 1
2 1
2 1
1 1
+
=
+






=
+
(
)
∫
∫
∫
−
−
x
x
dx
x
x
x
dx
x
x
dx
.
.
.
.
.
Then use elementary antiderivative formulas. To get the final answer, turn the
decimals in the denominators into fractions and simplify:
5
5 1 1
0 1
50
11
10
2 1
1 1
1 1
0 1
1 1
0 1
x
x
dx
x
x
C
x
x
−
−
−
−
+
(
) = −
+ −
+
= −
−
+
∫
.
.
.
.
.
.
.
.
C C
601.
2
9
2
3
5
4
9 2
3 2
4 5
x
x
x
C
−
+
+
Start by bringing all variables to the numerator. Then use elementary
antiderivative formulas:
x
x
x
dx
x
x
x
dx
x
x
x
7 2
1 2
1 5
7 2
1 2
1 5
9 2
3 2
4 5
1
9 2
3 2
4 5
−
+






=
−
+
(
)
=
−
+
+
∫
∫
−
C C
x
x
x
C
=
−
+
+
2
9
2
3
5
4
9 2
3 2
4 5
602.
−
+
1
2
cos x C
Use a trigonometric identity and simplify:
sin
cos
sin cos
cos
sin
cos
2
4
2
4
1
2
1
2
x
x
dx
x
x
x
dx
x dx
x C
∫
∫
∫
=
=
= −
+