Question

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

Answer 1

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

Answer 2

sorry I can't be much help here.

Answer 3

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

Answer 4

[-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]

Answer 5

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

Answer 6

someone please check i know its wrong

Answer 7

i assume you can work it from there? :)

Answer 8

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

Answer 9

the t goes down as you integrate up the sqrt part

Answer 10

but the t^3 might prove tricky

Answer 11

you sure that aint typoed?

Answer 12

I must us integration by parts

Answer 13

*use

Answer 14

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

Answer 15

May I see the full work out please

Answer 16

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

Answer 17

for the x square root problem

Answer 18

I think I am missing parts that is why

Answer 19

uv-integral vdu

Answer 20

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

Answer 21

.. 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 ...

Answer 22

No i know that

Answer 23

use the tabular method

Answer 24

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

Answer 25

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

that aint pretty ....

Answer 26

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

Answer 27

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

Answer 28

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

yuck

Answer 29

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

pretty

Answer 30

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

Answer 31

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