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Mathematics
Problem
The integral
∫
2
x
12
+
5
x
9
(
x
5
+
x
3
+
1
)
3
d
x
\int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx
∫
(
x
5
+
x
3
+
1
)
3
2
x
12
+
5
x
9
d
x
is equal to : (1)
−
x
5
(
x
5
+
x
3
+
1
)
2
+
C
\frac{-x^5}{(x^5 + x^3 + 1)^2} + C
(
x
5
+
x
3
+
1
)
2
−
x
5
+
C
(2)
x
10
2
(
x
5
+
x
3
+
1
)
2
+
C
\frac{x^{10}}{2(x^5 + x^3 + 1)^2} + C
2
(
x
5
+
x
3
+
1
)
2
x
10
+
C
(3)
x
5
2
(
x
5
+
x
3
+
1
)
2
+
C
\frac{x^5}{2(x^5 + x^3 + 1)^2} + C
2
(
x
5
+
x
3
+
1
)
2
x
5
+
C
(4)
−
x
10
2
(
x
5
+
x
3
+
1
)
2
+
C
\frac{-x^{10}}{2(x^5 + x^3 + 1)^2} + C
2
(
x
5
+
x
3
+
1
)
2
−
x
10
+
C
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