Question

integrate the following: indefinite integral [x squareroot(1+2x)]dx

Answer 1

u sub.

let u = 1+2x

Answer 2

once you have that, rewrite sqrt u = u^(1/2)

Answer 3

should be able to integrate using only the pwoer rule

Answer 4

do i need to find what x is in terms of u?

Answer 5

yes

Answer 6

once i do that then what? I'm confused on that part.

Answer 7

so far i have (u-1)/2 * u^1/2 * dx

Answer 8

u = 2x+1 => du = 2dx

=> x = (u-1)/2

so the integral becomes

\[\frac{ 1 }{ 2 } \int\limits \left( \frac{ u-1 }{ 2 } \right)\sqrt{u}\,\,du=\frac{ 1 }{ 2 } \int\limits \left( \frac{ u-1 }{ 2 } \right)u^{\frac{ 1 }{ 2 }}\,\,du=\frac{ 1 }{ 4 } \int\limits \left( u^{\frac{ 3 }{ 2 }}-u^{\frac{ 1 }{ 2 }} \right)\,\,du\]

Answer 9

Thank you! :)

Answer 10

you're welcome!