Question

Evaluate the integral by making the given substitutiohttp://www.webassign.net/cgi-bin/symimage.cgi?expr=int%20x%2A%2A%283%29%283%20%2B%20x%2A%2A%284%29%29%2A%2A5%20text%28%20%29%20dx%20text%28%2C%20%29%20u%20%3D%203%20%2B%20x%2A%2A%284%29

Answer 1

please show steps thanks in advance

Answer 2

\[u=3+x^4\]
\[du=4x^3 dx\]

Answer 3

yes and thank what?

Answer 4

*than

Answer 5

\[\frac{1}{4}\int{u^5}du\]

Answer 6

wait how did you get 1/4 from? and x^5?

Answer 7

ok never mind i know the u^5

Answer 8

but what did you do to get 1/4

Answer 9

As stated above, as \(u = 3+x^4\) then you have \[\frac{du}{dx}=4x^3\] or if you rearrange you have that \[du=4x^3 dx\] which gives you that \[x^3dx=\frac{1}{4}du\] So with this substitution that leaves you with \[\int x^3(3+x^4)^5 dx=\int x^3 (u)^5 dx = \int \frac{1}{4} u^5 du\] Now integrate with respect to u and get an answer. Then the last step is to take that answer, and any where u appears, replace it by what you substituted it for \(u=3+x^4\)

Answer 10

ok thanks ill take it from here