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Mathematics
Mathematics
Problem
If
I
=
∫
x
5
d
x
1
+
x
3
I = \int \frac{x^5 dx}{\sqrt{1+x^3}}
I
=
∫
1
+
x
3
x
5
d
x
, then I equals to - (A)
2
9
(
1
+
x
3
)
5
/
2
+
2
3
(
1
+
x
3
)
3
/
2
+
c
\frac{2}{9}(1+x^3)^{5/2} + \frac{2}{3}(1+x^3)^{3/2} + c
9
2
(
1
+
x
3
)
5/2
+
3
2
(
1
+
x
3
)
3/2
+
c
(B)
ln
∣
x
+
1
+
x
3
∣
+
c
\ln|\sqrt{x} + \sqrt{1+x^3}| + c
ln
∣
x
+
1
+
x
3
∣
+
c
(C)
ln
∣
x
−
1
+
x
3
∣
+
c
\ln|\sqrt{x} - \sqrt{1+x^3}| + c
ln
∣
x
−
1
+
x
3
∣
+
c
(D)
2
9
(
1
+
x
3
)
3
/
2
−
2
3
(
1
+
x
3
)
1
/
2
+
c
\frac{2}{9}(1+x^3)^{3/2} - \frac{2}{3}(1+x^3)^{1/2} + c
9
2
(
1
+
x
3
)
3/2
−
3
2
(
1
+
x
3
)
1/2
+
c
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