Use an appropriate method to evaluate each of the following indefinite integrals: A) the intergral of t^2 square root t^3 -1dt B) the intergral of square root (x)lnx dx PLEASE HELP Use an appropriate method to evaluate each of the following indefinite integrals: A) the intergral of t^2 square root t^3 -1dt B) the intergral of square root (x)lnx dx PLEASE HELP @Mathematics

For B set u=lnx and v=x^1/2 then use that substitution formula thing? I can't remember it...

sorry I can't be much help here.

Can someone please show the work out because I am just having problem on these few hw problems it will be of much help to me

[-t^2/sqr root of 6( (t^3-1)^(1/2)) - t/6(sqrt(t^3-1)^5) - 5 / 8sqrt ((t^3-1)^7) + c]

\[\int \sqrt{x}\ ln(x)\ dx\] \[\int\ (x)^{1/2}\ ln(x)\ dx\] \[=\frac{2x^{3/2}\ ln(x)}{3}-\int\ \frac{2x^{3/2}}{3x}\ \ dx\] \[=\frac{2x^{3/2}\ ln(x)}{3}-\frac{2}{3}\int\ x^{1/2}\ \ dx\]

someone please check i know its wrong

i assume you can work it from there? :)

\[\int t\sqrt{t^3-1}dt\] this is the same process, you appear to be working on integration by parts

the t goes down as you integrate up the sqrt part

but the t^3 might prove tricky

you sure that aint typoed?

I must us integration by parts

*use

if we use the sqrt part for going under we get hopefully not a mess... \[\int t\sqrt{t^3-1}dt\] \[=\frac{t^2}{2}\sqrt{t^3-1}-\int \frac{t^2}{2}\frac{3t^2}{2\sqrt{t^3-1}}dt\] that is nasty

May I see the full work out please

this is the "full work out" as far as i can tell ... if not im sure you are capable of filling in the peices

for the x square root problem

I think I am missing parts that is why

uv-integral vdu

the only thing your missing, might be the u du v dv nonesense that is just organization

.. and if your up to integration by parts and cant figure out the integral of x^(1/2) there aint much i can do for that ...

No i know that

use the tabular method

the "t" one tho, i got no clue about yet

\[\int t\sqrt{t^3-1}dt\] \[=t(\int' \sqrt{t^3-1}dt)-\int''(\sqrt{t^3-1}dt) \] that aint pretty ....

Because my professor told me to use integration by parts for this one

you sure it aint sqrt(t^2 -1) ??

http://www.wolframalpha.com/input/?i=integrate+t*sqrt%28t^3-1%29 yuck

http://www.wolframalpha.com/input/?i=integrate+t*sqrt%28t^2-1%29 pretty

you aint got the talent to do the first one, and neither do i unless thats a sqrt(t^2-1)

amistre what is the integral of sqrt[(t^3)-1]

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