Question

find the integral of (w divided by the quantity (1+w) raised to 3/4 ) dw

Answer 1

\[\int\frac{w}{(1+w)^{3/4}}dw\]

le \[u=1+w\Rightarrow du=dw\]

and \[u-1=w\]

\[\int\frac{w}{(1+w)^{3/4}}dw=\int\frac{u-1}{u^{3/4}}du=\int(u-1)u^{-3/4}du\]

\[=\int\left(u^{1/4}-u^{-3/4}\right)du=\cdots\]