The correct option is A 25√(5x+8)+c Put = 5x + 8 = t^2 5dx = 2t dt #160; dx = 25 t dt 25∫tt dt 25 t + c = 2/5√(5x + 8) ...

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Section Formula

Evaluate: ∫d...

Question

Evaluate:
$\int \frac{d x}{\sqrt{5 x + 8}}$

\frac{2}{5} \sqrt{5 x + 8} + c

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- \frac{2}{5} \sqrt{5 x + 8} + c

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\frac{1}{5} \sqrt{5 x + 8} + c

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- \frac{1}{5} \sqrt{5 x + 8} + c

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Solution

The correct option is A $\frac{2}{5} \sqrt{5 x + 8} + c$
Put $= 5 x + 8 = t^{2}$
$5 d x = 2 t d t$
$d x = \frac{2}{5} t d t$
$\frac{2}{5} \int \frac{t}{t} d t$
$\frac{2}{5} t + c$
$= \frac{2}{5} \sqrt{5 x + 8} + c$

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