Step $3$

Now, if $u=50+e^x,$ then ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^x\sqrt[\phantom{2}]{50+e^x}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{u}du={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{\frac{1}{2}}du.$

This evaluates as ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{\frac{1}{2}}du=+C$

$$