Question

\[\int\limits_{0}^{1} x^2 (x^2 + 1)^3 dx\]

find the antiderivative please

Answer 1

those are all powers of 3 right?

Answer 2

yes

Answer 3

ok

Answer 4

\[\int\limits_{0}^{1}x ^{3}(x ^{3}+1)(x ^{3}+1))x ^{3}+1)dx \rightarrow \int\limits_{0}^{1}(x ^{6}+x ^{3})(x ^{3}+1)(x ^{3}+1) \]

Answer 5

\[\int\limits_{0}^{1}(x ^{9}+2x ^{6}+x ^{3})(x ^{3}+1)dx \rightarrow \int\limits_{0}^{1}(x ^{12}+3x ^{9}+3x ^{6}+x ^{3})dx\]

Answer 6

\[\frac{ x ^{13} }{ 13 }+\frac{ 3x ^{10} }{ 10 }+\frac{ 3x ^{7} }{ 7 }+\frac{ x ^{4} }{ 4 } = \frac{ 1 }{ 13 }+\frac{ 3 }{ 10 }+\frac{ 3 }{ 7 }+\frac{ 1 }{ 4 }\]

Answer 7

you see everything? Just tedious.

Answer 8

And I also didnt feel like using integration by parts.

Answer 9

expanding into a poly works ... time consuming, but it works ;)

Answer 10

amistre is there another way to do it besides integration by parts?

Answer 11

im sure there is, but if they are asking for an "antiderivative", then your setup was what they expected