Question

x/underroot x+2 integration

Answer 1

[tex] \int\limits^a_b { \frac{x}{ \sqrt{x+2} } } \, dx \\ \\ t = \sqrt{x+2} \\ \\ x = t^{2} - 2 \\ \\ dx = 2 t dt \\ \\ \int\limits^a_b {\frac{t^{2}-2}{t}} \, 2tdt \\ \\ \int\limits^a_b {(2t^{2} - 4)} \, dt \\ \\ \frac{2t^{3}}{3} - 4 t + C \\ \\ \frac{2(x+2)^{3/2}}{3} - 4 \sqrt{x+2} + C[/tex]

Answer 2

 [tex] \int\limits^a_b { \frac{x}{ \sqrt{x+2} } } \, dx
t^2=x+2
 \int\limits^a_b {1} \, dx =2tdt
x=t^2-2
= \int\limits^a_b { \frac{t^2-2}{t} } \, 2tdt
 \int\limits^a_b {2t^2-4} \, dt
= \frac{2t^3}{3} -4t+C
= \frac{2(x+2)^3^/^2}{3} -4 \sqrt{x+2} +C