Question

I need help with tis integral ln x/sqrt x dx we are using the method let u= and dv=

Answer 1

so you are using integration by parts

Answer 2

lnx is usually a sure bet for u

Answer 3

1/sqrt(x) is simple enough to integrate into v

Answer 4

you end up with a -int 2sqrt(x)/x which is powerable

Answer 5

Yes we are using integration by parts. I found lots of examples but none that involved fractions so that is why I am having trouble.

Answer 6

integrate x^(-1/2) what do you get?

Answer 7

you should be comfortable with the power rule for integration

Answer 8

-(1/2)-3/2

Answer 9

\[\int x^n\to \frac{x^{n+1}}{n+1}\]

Answer 10

x(-1/2+1)/ (-1/2+1)= x^0.5/0.5

Answer 11

\[\binom{u=ln(x)}{du=\frac{1}{x}dx}\ \binom{v=2x^{1/2}}{dv=x^{-1/2}dx}\]
\[\int udv=uv-\int vdu\]

Answer 12

correct

Answer 13

yes

Answer 14

\[-\int vdu\to -\int 2x^{1/2}x^{-1}dx = -\int 2x^{-1/2} dx\]