Question

Integration Procedures(Itevrations by Parts)

∫ y √(y+1)dy

Answer 1

$$\int y\sqrt{(y+1)}dy=\int (y+1-1)\sqrt{(y+1)}dy$$

$$=\int (y+1)^{3/2}dy-\int \sqrt{(y+1)}dy$$

$$=\dfrac{2}{5} (y+1)^{5/2}-\dfrac{2}{3} (y+1)^{3/2}+C$$

$$=\dfrac{2}{15} (y+1)^{3/2}(3y+3-5)+C$$

$$=\dfrac{2}{15} (y+1)^{3/2}(3y-2)+C$$