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How can I solve the following? (attached)

Mathematics
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Sample problem:
What step are you confused on the sample problem?

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Other answers:

I understand the sample problem. I just don't know how to use it for the actual problem.
do the same...instead of using 7 use 5
I did, but it shows up as wrong when I put it in.
then you did something wrong. ...show me the steps
what is the final answer that you got when you did the problem?
Nevermind, I found my error, instead of 2/9 I put 2/5. Sorry. Can you help me with another problem though?
yes sure....remember to follow all the steps and make sure you don't make a mistake. One small mistake can make the answer wrong
What's the first step? Let's make the square root into an exponent \[\int\limits_{3}^{7}\frac{1}{\sqrt{6x+7}}dx\]\[\int\limits_{3}^{7}\frac{1}{(6x+7)^\frac{1}{2}}dx\]
then we bring the denominator to the top. But in order to do this we have to make the exponent a negative. Then we get \[\int\limits_{3}^{7}(6x+7)^{-\frac{1}{2}}dx\]
You just integrate what's inside first....can you tell me what you get?
3x^2+7x+C
No that's not it. Look back in the problem you did before and see how they integrated a square root after it became \[(-------)^\frac{1}{2}\]
you have to do the chain rule.
Try it one more time....what is the integral?
I have no idea here..
I thought you know how to integrate something that was a square root. Look at the example problem you did before and see what happens.
Would it be: 1/12 root of 6x+7?
Is the answer 1/4? If yes, then I've done my work correct.
I think you made a mistake \[\frac{1}{6} *\frac{1}{2}=\frac{1}{12}\] that's how you got the 12 right?
Yes
it's suppose to be\[\frac{1}{6}*2=\frac{2}{3}=\frac{1}{3}\]
1/3 root of 6x+7 not 1/12 root of 6x+7
Oh, so then the answer would be: 1.
what no I got something else
\[\frac{1}{3}\sqrt{6x+7}\]\[\frac{1}{3}\sqrt{6(7)+7}-\frac{1}{3}\sqrt{6(3)+7}\]
\[\frac{1}{3}(\sqrt{6(7)+7}-\sqrt{6(3)+7})\]\[\frac{1}{3}(\sqrt{42+7}-\sqrt{18+7})\]
can you do the rest?
Yes, I got it.
what did you get?
Im doing the math right now.
ok tell me what you get just to check if you got it right.
2/3
yeah that's what I got good job.
If you have more problems post them in a different question.
I want to give you more medals :) for the good job

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