Question

Integral help please!

Answer 1

Find the integral. Assume b is a constant greater than 1.
\[\int\limits_{}^{}b^{x}(1+b^{x})^{4}dx\]

Answer 2

you can use Binomial theorem.

Answer 3

\[ let~u = 1+b^x\rightarrow du=ln |b|* b^xdx\\\frac{du}{ln|b|}=b^xdx\]

Answer 4

it turns
\[\int \frac{1}{ln|b|}u^4du\]

Answer 5

ok, it's correct. now, take integral , that's it

Answer 6

@Loser66 Okay, so then I'm seeing that the integral would be
\[\frac{ u^{5} }{ 5 }*\frac{ x }{ \ln \left| 2 \right| }\]

Answer 7

how do you get ln|2| ? why do you have x in numerator? You just have u^5/5ln|b| +C
and then plug u = 1+b^X you have the final answer is \[\frac{(1+b^x)^5}{5ln|b|}\]that's it

Answer 8

Oh, okay. Thank you so much!