Question

Solve for this integral question

Answer 1

Answer:

$\frac{(5+2x)^{3/2} }{3}$

Step-by-step explanation:

Use u-substitution.

Let u=5+2x

∴$\frac{du}{dx}$=2

∴du=2dx

$\int\limits {\sqrt{5+2x} } \, dx$

$\int\limits {(\sqrt{5+2x} (1/2) (2)} \, dx$ (because (1/2)(2)=1)

$\int\limits {(\sqrt{u}) (1/2) } \, du$ (because 5+2x=u, and 2dx=du)

(1/2) $\int\limits {(\sqrt{u}) } \, du$ (because $\int\limits {xa} \,$=$a\int\limits {x} \,$)

(1/2) $\int\limits {(u^{1/2} ) } \, du$

(1/2) ($u^{3/2}$/(3/2))

(1/2) (2$u^{3/2}$/3)

$\frac{u^{3/2} }{3}$

u=5+2x, so $\int\limits {\sqrt{5+2x} } \, dx$ =

$\frac{(5+2x)^{3/2} }{3}$