Question

Calculus 2 i need help integrating a problem. (1/(y+2sqrt.(y)))dy. I tried seperating it into two different fractions and integrating but apperently that is wrong. Any ideas? Thanks. :)

Answer 1

\[\int\frac{\mathrm dy}{y+2\sqrt y}\]Suppose you let \(x=\sqrt y\), which would mean \(x^2=y\) and \(2x\,\mathrm dx=\mathrm dy\). Then the integral can be rewritten as
\[\int\frac{2x}{x^2+2x}\,\mathrm dx=2\int\frac{\mathrm dx}{x+2}\]