Question

Can someone please give me a step by step solution for this?

Answer 1

\(\large \begin{align} \color{black}{
\int \dfrac{4}{(x+y)^2}\,dy \hspace{.33em}\\~\\
=4 \int \dfrac{1}{(x+y)^2}\,dy \hspace{.33em}\\~\\
\normalsize \text{put x+y=t} \hspace{.33em}\\~\\
x+y=t \hspace{.33em}\\~\\
\frac{d}{dy}\left(x \right)+\frac{d}{dy}\left(y \right)=\frac{d}{dy}\left(t \right) \hspace{.33em}\\~\\
dy=dt \hspace{.33em}\\~\\
=4 \int \dfrac{1}{(t)^2}\,dt \hspace{.33em}\\~\\
=4 \left(- \dfrac{1}{(t)} \right) \hspace{.33em}\\~\\
= \left(- \dfrac{4}{(x+y)} \right)+C \hspace{.33em}\\~\\
}\end{align}\)