Question

you want to evaluate the integral 4x^2(3x-x^3)^5 dx using substituiton.
which of the following is the best choice for the substitution variable u?

Answer 1

is u=4x^2?

Answer 2

or u=3x-x^3
u=(3x-x^3)^5
u=x^2(3x-x^3)^5

Answer 3

I think this needs to be expanded, then integrated.

Answer 4

\[4 x^2 \left(3 x-x^3\right)^5=-4 x^{17}+60 x^{15}-360 x^{13}+1080
x^{11}-1620 x^9+972 x^7
\]

Answer 5

\[\int \left(-4 x^{17}+60 x^{15}-360 x^{13}+1080 x^{11}-1620 x^9+972
x^7\right) \, dx=\\-4 \left(\frac{x^{18}}{18}-\frac{15
x^{16}}{16}+\frac{45 x^{14}}{7}-\frac{45 x^{12}}{2}+\frac{81
x^{10}}{2}-\frac{243 x^8}{8}\right)
\]