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January 29, 2015

January 29, 2015

Posted by **Erica** on Tuesday, October 18, 2011 at 8:45pm.

∫ from 1 to 4 of (√x) (ln√x) dx

Im not really sure what to choose for u and dv.

Thank you so much for the help!!

- Calc -
**Steve**, Wednesday, October 19, 2011 at 5:32amTry to set u to something that gets simpler in the derivative.

u = ln √x

du = 1/√x * 1/2√x dx = dx/2x

dv = √x

v = 2/3 x^{3/2}

∫ u dv = uv - ∫v du

= 2/3 x^{3/2}ln √x - ∫ 1/3 √x dx

= 2/3 x^{3/2}ln √x - 2/9 x^{3/2}

= 2/9 x^{3/2}(3 ln √x - 1)

F(4) = 16/9 (ln 8 - 1)

F(1) = -2/9

F(4) - F(1) = 16/9 ln 8 - 14/9

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