## anonymous 4 years ago Find the antiderivative of: ln/√ y

1. anonymous

(x(log(x)-1)/ √y) + C

2. anonymous

$y*\ln \sqrt{y} -0.5*y$

3. TuringTest

what is the problem? can you use the equation editor please?

4. anonymous

$\int\limits_{4}^{9} \ln(y)/\sqrt{y}$

5. TuringTest

Here's the indefinite integral: integration by parts$u=\ln y$$dv=y^{-1/2}$$\int y^{-1/2}\ln y=2y^{1/2}\ln y-\int2y^{1/2}\cdot(\frac1y)dy$$=2y^{1/2}\ln y-2\int y^{-1/2}dy=2y^{1/2}\ln y-4y^{1/2}+C$$=2\sqrt y(\ln y-2)+C$with the definite integral you would just evaluate at the end and remove the C