Question

usind integration by substitution what is the integral of (2x+1)(x^2+x+1)^7

Answer 1

intrinsic philosophy

Answer 2

Again, make the higher order term = u and the lower as du, i.e.,
u = x^2 + x + 1
du = (2x + 1)dx

Answer 3

then it will become a power rule integration of the form:\[\int\limits_{a}^{b}u^{7}du\]

Answer 4

let u=x^2+x+1, du = 2x+1, so integral of 1/(u)^7du, so its' 1/8(u)^8, sub u back in u get 1/8(x^2+x+1)+c

Answer 5

bmp, u mean 1/u^7 ?

Answer 6

Nope, that's a multiplication. If it was a division, we would've gotten a natural log integration pattern.

Answer 7

aa, i completely saw a division sign -.- i must be tired lol

Answer 8

lol we're all seeing division signs @_@

Answer 9

got some error with my division one 2... =/

Answer 10

first time doing a ques. like this..can some 1 show me all the steps...this is where i am so far

Answer 11

Your du term is incorrect, you most likely committed a minor mistake there. It should be du = (2x+1)dx, not otherwise. And, yes, the integral will be of the form\[\frac{u^{8}}{8} + c\]where u = x^2 + x + 1

Answer 12

\[\int\limits_{}^{}(2x+1)(x ^{2}+x+1)^{7}dx\]
u=\[x ^{2}+x+1\]
du=2x+1
\[\int\limits_{}^{}u ^{7}du\]
(1\[(1\div8)u ^{8}+c\]
\[(1\div8)(x ^{2}+x+1)^{8}+c\]