Evaluating the Integral of 6ln(x^2-9)

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Homework Statement

intrgral of 6ln(x^2-9)





solution

6((x+3)ln(x+3)-(x+3)+(x-3)ln(x-3)+ln(x-3))+c

check if it is right?
 
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yaho8888 said:
Homework Statement

intrgral of 6ln(x^2-9)





solution

6((x+3)ln(x+3)-(x+3)+(x-3)ln(x-3)+ln(x-3))+c

check if it is right?


almost correct except last term should be -(x-3) instead of ln(x-3)
 
Why is ln(x-3)?
 
yaho8888 said:
Why is ln(x-3)?

no i said it should be -(x-3) put the error in Bold
 
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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