intdx32 2x^2 =12∫dx16 x^2 =12∫dx(4)^2 x^2 =12.12×4log|4+x4 x|+C =116log|4+x4 x|+C ...

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Integration by Substitution

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Question

Evaluate: $\int \frac{d x}{32 - 2 x^{2}}$

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Solution

$i n t \frac{d x}{32 - 2 x^{2}} = \frac{1}{2} \int \frac{d x}{16 - x^{2}} = \frac{1}{2} \int \frac{d x}{(4)^{2} - x^{2}} = \frac{1}{2} . \frac{1}{2 \times 4} l o g | \frac{4 + x}{4 - x} | + C = \frac{1}{16} l o g | \frac{4 + x}{4 - x} | + C$

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