Question

integral from x to lnx (t^2 + 3)dt Please show steps.

Answer 1

Ok give me a sec to type it out

Answer 2

Awesome, thanks.

Answer 3

did you mean "t" to "ln(t)" ? otherwise T is just a constant

Answer 4

Yes

Answer 5

\[\int\limits_{X}^{\ln X}(t^2+3)dt\]=\[[\frac{t^3}{3}+3t] \]evaluated from x to ln x (this is just the power rule)
= \[(\frac{(\ln x)^3}{3}+3(\ln x))-(\frac{x^3}{3}+3x)\]
= \[\frac{(\ln x)^3}{3}+3(\ln x)-\frac{x^3}{3}-3x\]

Answer 6

Pretty good @kirbykirby

Answer 7

Thanks for the help!

Answer 8

yw