Let #160; I=∫( 2x+5 ) dx x ^ 2 +5x 3 #160; Let #160; #160; log| x ^ 2 +5x 3 | =Z So, on differentiating, we get 2x+5 x ^ 2 +5x 3 dx=dz ...

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Integration by Substitution

∫2x+5/x2+5x-3...

Question

$\int \frac{2 x + 5}{x^{2} + 5 x - 3} d x$

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Solution

Let $I = \int \frac{(2 x + 5) d x}{x^{2} + 5 x - 3}$
Let $l o g ∣ ∣ x^{2} + 5 x - 3 ∣ ∣ = Z$
So, on differentiating, we get
$\frac{2 x + 5}{x^{2} + 5 x - 3} d x = d z$
So, $I = \int d Z = Z + C = l o g ∣ ∣ x^{2} + 5 x - 3 ∣ ∣ + C$

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