Help please???? Integral from 0 to 2 of d/dx*(ln(x+1)/x^3)dx

[mbart42]

Integral from 0 to 2 of d/dx*(ln(x+1)/x^3)dx

Find the 2014th nonzero term for f(x)=x/(x^3-1)^2

Integral from 0 to infinity of lnx/(x^2+x+1)dx

help is much appreciated! Thank you!

 

[Deleted member 4993]

Integral from 0 to 2 of d/dx*(ln(x+1)/x^3)dx

Find the 2014th nonzero term for f(x)=x/(x^3-1)^2

Integral from 0 to infinity of lnx/(x^2+x+1)dx

help is much appreciated! Thank you!

What are your thoughts?

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[mbart42]

For the first one, I evaluated at 2 to get ln3/8 but am not sure what to do next because when 0 is put in it is undefined

For the second one so far I assume it as geometric and put it as the summation of -(x^3)^n, but am not sure what to do considering in the parentheses is a equation and not a number

for the third one I attempted to integrate it but was unable to due to the natural log.

 

[stapel]

\(\displaystyle \displaystyle \mbox{1. }\, \int_0^2\, \dfrac{d}{dx}\, \left(\dfrac{\ln(x\, +\, 1)}{x^3}\right)\, dx\)

I evaluated at 2 to get ln3/8 but am not sure what to do next because when 0 is put in it is undefined

What did you evaluate? Are you saying that you did the integration? If so, what did you get? If not, what did you do?

\(\displaystyle \displaystyle \mbox{2. Find the 2014th non-zero term for }\, f(x)\, =\, \dfrac{x}{(x^3\, -\, 1)^2}\)

I assume it as geometric and put it as the summation of -(x^3)^n, but am not sure what to do considering in the parentheses is a equation and not a number

You assumed what was geometric? What does your book mean by "the 2014th...term for" the rational function? Were you maybe supposed to express the function in some non-rational format? If so, what, exactly, were the instructions for this? If not, what were the rest of the instructions, which explain the part that you've posted?

\(\displaystyle \displaystyle \mbox{3. } \int_0^{\infty}\, \dfrac{\ln(x)}{x^2\, +\, x\, +\, 1}\, dx\)

I attempted to integrate it but was unable to due to the natural log.

Use the method they taught you in class and in the book; namely, taking limits.