∫( x+2√( x 3 ) #160; ) #160; dx =∫ x dx+2∫√( x 3 ) #160; dx = x ^ 2 2 +2( x 3 ) #160; ^ 3/2 3/2 +c = x ^ 2 2 + 4 3 ( x 3 ) ...

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Integration by Substitution

∫x+2√x-3dx

Question

$\int x + 2 \sqrt{x - 3} d x$

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Solution

$\int (x + 2 \sqrt{x - 3}) d x$
$= \int x d x + 2 \int \sqrt{x - 3} d x$
$= \frac{x^{2}}{2} + 2 \frac{{(x - 3)}^{3 / 2}}{3 / 2} + c$
$= \frac{x^{2}}{2} + \frac{4}{3} {(x - 3)}^{3 / 2} + c$

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