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Integral help!!!!! Calculus!!!?

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∫ 1 / (2 + sqrt(2x)) dx

definite-integral

asked Apr 24, 2013 in CALCULUS by linda Scholar

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$integral fraction numerator 1 over denominator 2 plus square root of 2 x end root end fraction d x equal integral fraction numerator square root of 2 square root of x over denominator 2 plus t end fraction d t$ (Let $square root of 2 x end root space equal t space t h e n square root of 2 fraction numerator 1 over denominator 2 square root of x end fraction d x equal d t space o r space d t equal fraction numerator 1 over denominator square root of 2 x end root end fraction d x$ )

$space space space space space space space space space space space space space space space space space space space space space space equal integral fraction numerator t over denominator 2 plus t end fraction d t$

$space space space space space space space space space space space space space space space space space space space space space space equal integral fraction numerator 2 plus t minus 2 over denominator 2 plus t end fraction d t$

$space space space space space space space space space space space space space space space space space space space space space space equal integral fraction numerator 2 plus t over denominator 2 plus t end fraction d t minus 2 integral fraction numerator 1 over denominator 2 plus t end fraction d t$

$space space space space space space space space space space space space space space space space space space space space space space equal integral d t minus 2 integral fraction numerator 1 over denominator 2 plus t end fraction d t$

space space space space space space space space space space space space space space space space space space space space space space equal t minus 2 italic log open parentheses open vertical bar 2 plus t close vertical bar close parentheses plus C

space space space space space space space space space space space space space space space space space space space space space space equal square root of 2 x end root minus 2 italic log open parentheses open vertical bar 2 plus square root of 2 x end root close vertical bar close parentheses plus C (Substitute t equal square root of 2 x end root )