Mathematics

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


SOLUTION
Let $$I=\int { \dfrac { \left( 2x+5 \right) dx }{ { x }^{ 2 }+5x-3 }  } $$
Let  $$log\left| { x }^{ 2 }+5x-3 \right| =Z$$
So, on differentiating, we get
$$\dfrac { 2x+5 }{ { x }^{ 2 }+5x-3 } dx=dz$$
So, $$I=\int { dZ } =Z+C=log\left| { x }^{ 2 }+5x-3 \right| +C$$
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Subjective Medium Published on 17th 09, 2020
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