Question

how do we integrate
(y^(1/2))/(y+1)

Answer 1

what is this geometry

Answer 2

Change the variable to
\[
u=\sqrt y\\
du= \frac {dy}{2 \sqrt y}\\
dy =2 \sqrt y du= 2 u du\\
\]

Answer 3

\[
\int \frac{\sqrt{y}}{y+1} \, dy=\int\frac{2 u^2 du}{u^2+1}=\\
\int\left(2-\frac{2}{u^2+1}\right)du= 2 u - 2 \tan^{-1}u + C\\
2 \sqrt{y}-2 \tan ^{-1}\left(\sqrt{y}\right)+C
\]

Answer 4

thank u
that helps me ;-)

Answer 5

YW