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Theorems for Differentiability

Evaluate: ∫2...

Question

Evaluate:
$\int \frac{2 x + 5}{x^{2} + 5 x + 6} d x$

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Solution

$\int \frac{2 x + 5}{x^{2} + 5 x + 6} d x$

Let $t = x^{2} + 5 x + 6 ⟹ d t = 2 x + 5 d x$

$= \int \frac{1}{t} d t$

$= log t + c$

put value of $t$

$= log (x^{2} + 5 x + 6) + c$

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