Answer:
[tex]\frac{(5+2x)^{3/2} }{3}[/tex]
Step-by-step explanation:
Use u-substitution.
Let u=5+2x
∴[tex]\frac{du}{dx}[/tex]=2
∴du=2dx
[tex]\int\limits {\sqrt{5+2x} } \, dx[/tex]
[tex]\int\limits {(\sqrt{5+2x} (1/2) (2)} \, dx[/tex] (because (1/2)(2)=1)
[tex]\int\limits {(\sqrt{u}) (1/2) } \, du[/tex] (because 5+2x=u, and 2dx=du)
(1/2) [tex]\int\limits {(\sqrt{u}) } \, du[/tex] (because [tex]\int\limits {xa} \,[/tex]=[tex]a\int\limits {x} \,[/tex])
(1/2) [tex]\int\limits {(u^{1/2} ) } \, du[/tex]
(1/2) ([tex]u^{3/2}[/tex]/(3/2))
(1/2) (2[tex]u^{3/2}[/tex]/3)
[tex]\frac{u^{3/2} }{3}[/tex]
u=5+2x, so [tex]\int\limits {\sqrt{5+2x} } \, dx[/tex] =
[tex]\frac{(5+2x)^{3/2} }{3}[/tex]
