Differentiate, but do not simplify: ##y=3ln(4-x+5x^2)##

ttpp1124
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Homework Statement
can someone check to see if my work is correct?
Relevant Equations
n/a
IMG_4238.jpg
 
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It looks like there's a "u" term in your answer but none in the original problem. A typo?
 
DaveE said:
It looks like there's a "u" term in your answer but none in the original problem. A typo?
please excuse me horrible writing, it's supposed to be a 4
 
OK, then I'm happy. I'm not sure about the do not simplify part, it looks pretty simple already!
 
ttpp1124 said:
please excuse me horrible writing, it's supposed to be a 4

A solution to this problem is by using Latex. It is really not that hard: write what you would expect and put it between double hashtags:

I promise we will be there to help you learn it if you struggle!
 
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What part of this calculation were you not confident about? Why do you ask, instead of knowing you are correct?
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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