How do you integrate $\int x \sqrt{2 x + 1} d x$ $int xsqrt(2x+1)dx$ ?

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Answer 1 · 2017-01-30T17:27:32

$\frac{1}{15} {(2 x + 1)}^{\frac{3}{2}} (3 x - 1) + C .$ $1/15(2x+1)^(3/2)(3x-1)+C.$

Let $2x+1=t^2 :. x=(t^2-1)/2, and, dx=tdt.$

Therefore, the Reqd. Integral $=int{((t^2-1)/2)(sqrtt^2)(t)}dt$

$=1/2int(t^4-t^2)dt=1/2(t^5/5-t^3/3)=t^3/30(3t^2-5)$

$=1/30(t^2)^(3/2)(3t^2-5)$

$=1/30(2x+1)^(3/2){3(2x+1)-5}$

$=1/15(2x+1)^(3/2)(3x-1)+C.$

How do you integrate int xsqrt(2x+1)dx∫x√2x+1dxint xsqrt(2x+1)dx?