Question

http://www.webassign.net/cgi-perl/symimage.cgi?expr=int%20a%5Ex%20%281%20%2B%20a%5Ex%29%5E%284%29%20text%28%20%29dx&size=4

Find the integral. Assume a is a constant greater than 1.

Answer 1

let \(a^x = u\)

lnu = xlna

du = a^x lna dx
du/lna = a^x dx

\(\LARGE \frac{1}{lna} \int (1 + u)^4 du\)

let s = 1 + u

\(\LARGE \frac{1}{lna} \int (s)^4 du\)

\(\LARGE \frac{1}{lna} \frac{s^5}{5}\)

\(\LARGE \frac{1}{lna} \frac{(1 + u)^5}{5}\)

\(\LARGE \frac{(1 + x\ln a)^5}{5\ln a}\)

Answer 2

oops im wrong...that's supposed to be \(\Large \frac {(1 + a^x)^5}{5\ln a}\)

Answer 3

i misread what i let u equal to a while ago when i substituted back

Answer 4

Liar^

Answer 5

so what does "constant greater than 1" changes?

Answer 6

it means that the answer exists because if a = 1 then the denominator would be 5 ln(1) = 0 and would be undefined

Answer 7

i keep getting \[(a^x(10a^(2x)+5a^(3x)+z^(ax)+10a^x+5)\div(5\ln(a))\]

Answer 8

well...i gave you the solution...compare it with yours and see where you're going wrong

Answer 9

since she answered your question she should get what was promised lol

Answer 10

she will ;)

Answer 11

for the sake of it..let's check \(\Large \frac{(1 + a^x)^5}{5 lna}\)

\(\Large \frac{5(1 + a^x)^4}{5 lna} (a^x \ln a)\)
\(\Large \frac{\cancel{5}(1 + a^x)^4}{\cancel{5}\cancel{\ln a}} (a^x \cancel{\ln a})\)

so we have

\((1 + a^x)^4 a^xdx \checkmark\)

Answer 12

how do you write the equations like that?

Answer 13

thats so much easy to understand

Answer 14

latex haha but it's kinda hard to type =))

Answer 15

@Ldaniel ?