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ChrisVBest ResponseYou've already chosen the best response.0
\[\int\limits_{?}^{?}(x+1)5^(x+1)^2\]
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
that (x+1)^2 is an exponent
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
\[ \int(x+1)5^{(x+1)^2}dx \]That?
 one year ago

.Sam.Best ResponseYou've already chosen the best response.1
\[\Huge \int\limits_{}^{}(x+1)(5)^{(x+1)^2}\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.1
substitution u==x+1 du=dx \[\text{}=\int\limits 5^{u^2} u \, du\] substitution again t=u^2 dt=2udu \[\frac{1}{2}\int\limits 5^t \, dt\] \[\frac{5^t}{2 \ln (5)}+c\] \[\frac{5^{(x+1)^2}}{\log (25)}+c\]
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
Okay, so u=x+1 and we have \[ \int u\cdot 5^{u^2}du=\int u\cdot e^{u^2\log5}du=\frac{1}{2\log 5}\int 2\log5u\cdot e^{u^2\log5}du=\frac{e^{u^2\log5}}{2\log 5}=\frac{5^{(x+1)^2}}{2\log5} \]
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
Oh, Sam's way is a little easier.
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
well the answer the book gives me looks like
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
\[1/2(5^{(x+1)^2}/\ln5)+C\]
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
Yep, that's the exact same thing as my answer and Sam's answer, just written slightly different.
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
i just dont understand how they get to that
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
Which part of the method Sam and I used did you not follow? (Sam's is a bit easier to follow because he does substitution twice and I only used it once)
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
i understand u substitution
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
5^u^2 = (ln5)u^2 right?
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
\[ 5^{u^2}=e^{(\log5)u^2} \]
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
\[ \int a^xdx=\int e^{x\log a}dx=\frac{1}{\log a}\int(\log a) e^{x\log a}dx=\frac{e^{x\log a}}{\log a}=\frac{a^x}{\log a} \\\int a^xdx=\frac{a^x}{\log a} \]
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
ok here is where im confused
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
how does 5^t become 5^t/ln5
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
He integrates it, using the formula I derived in my last comment.
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
well thats where im lost. I do not know how to integrate that
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
\[1/2\int\limits5^t dt\]
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
i would say that that is (ln5)t
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
and obviously im wrong lol
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
I just showed you how to integrate that in my comment, did you not see that? For \(a\) as any constant.
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
\[\int a^xdx=\int e^{x\log a}dx=\frac{1}{\log a}\int(\log a) e^{x\log a}dx=\frac{e^{x\log a}}{\log a}=\frac{a^x}{\log a} \\\int a^xdx=\frac{a^x}{\log a}\]
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
k ill write that down and try to wrap my brain around it
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
some things are just beyond me i guess
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
You just have to remember that \(e^{x^y}=e^{xy}\), which makes it so that \(a^x=(e^{\log a})^x=e^{x\log a}\)
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
Sorry, that first part should read \((e^x)^y=e^{xy}\)
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
luckily i have a 99.8 average in this class so if i miss this on the final it shouldnt hurt much >.<
 one year ago

nbouscalBest ResponseYou've already chosen the best response.2
Just revisit the rules for differentiating/integrating exponential and logarithmic functions. They come in handy for a lot of tricky integrals.
 one year ago

ChrisVBest ResponseYou've already chosen the best response.0
i try, i think my brain is overloaded. It is finals week
 one year ago
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