Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits_{?}^{?}(x+1)5^(x+1)^2\]
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
that (x+1)^2 is an exponent
 2 years ago

nbouscal Group TitleBest ResponseYou've already chosen the best response.2
\[ \int(x+1)5^{(x+1)^2}dx \]That?
 2 years ago

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

.Sam. Group TitleBest 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 \[\frac{1}{2}\int\limits 5^t \, dt\] \[\frac{5^t}{2 \ln (5)}+c\] \[\frac{5^{(x+1)^2}}{\log (25)}+c\]
 2 years ago

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

nbouscal Group TitleBest ResponseYou've already chosen the best response.2
Oh, Sam's way is a little easier.
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
well the answer the book gives me looks like
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
\[1/2(5^{(x+1)^2}/\ln5)+C\]
 2 years ago

nbouscal Group TitleBest 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.
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
i just dont understand how they get to that
 2 years ago

nbouscal Group TitleBest 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)
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
i understand u substitution
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
5^u^2 = (ln5)u^2 right?
 2 years ago

nbouscal Group TitleBest ResponseYou've already chosen the best response.2
\[ 5^{u^2}=e^{(\log5)u^2} \]
 2 years ago

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
ok here is where im confused
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
how does 5^t become 5^t/ln5
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
in sams answer
 2 years ago

nbouscal Group TitleBest ResponseYou've already chosen the best response.2
He integrates it, using the formula I derived in my last comment.
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
well thats where im lost. I do not know how to integrate that
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
\[1/2\int\limits5^t dt\]
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
i would say that that is (ln5)t
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
and obviously im wrong lol
 2 years ago

nbouscal Group TitleBest 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.
 2 years ago

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

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
k ill write that down and try to wrap my brain around it
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
some things are just beyond me i guess
 2 years ago

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

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

ChrisV Group TitleBest 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 >.<
 2 years ago

nbouscal Group TitleBest 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.
 2 years ago

ChrisV Group TitleBest ResponseYou've already chosen the best response.0
i try, i think my brain is overloaded. It is finals week
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.