Question

integrate x sqrt(2x-1)

Answer 1

show steps plz

Answer 2

let u =2x-1 --> du = 2 dx or du/2 =dx
replace to the original one and take integral respect to u

Answer 3

If it wasn't clear, since \(u=2x-1\), then you have \(x=\dfrac{u+1}{2}\).

Answer 4

plz show *all* steps

Answer 5

Using the sub suggested by @Loser66, \[\int x\sqrt{2x-1}~dx~\Rightarrow~\int\frac{u+1}{2}\sqrt u~du\]
Factor out the 1/2, then distribute the \(\sqrt u\). You get
\[\frac{1}{2}\int\left(u^{3/2}+u^{1/2}\right)~du\]

Answer 6

still not getting it

Answer 7

integrate of (u^3/2) = 2/5 u^5/2 and integrate of (u^1/2) = 2/3 u ^3/2

Answer 8

replace u with 2x - 1, and remember to add C as constant in there