Evaluate the following intregals: 6x-5 3x^2-5x+1 dx - Vidyadip

Question

Evaluate the following intregals:
$\int\frac{6\text{x}-5}{\sqrt{3\text{x}^2-5\text{x}+1}}\text{ dx}$

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Answer

Let $\text{I}=\int\frac{6\text{x}-5}{\sqrt{3\text{x}^2-5\text{x}+1}}\text{ dx}$
putting $3\text{x}^2-5\text{x}+1=\text{t}$
$\Rightarrow(6\text{x}-5)\ \text{dx}=\text{dt}$
Then,
$\text{I}=\int\frac{\text{dt}}{\sqrt{\text{t}}}$
$=2\sqrt{\text{t}}+\text{C}$
$=2\sqrt{3\text{x}^2-5\text{x}+1}+\text{C}$

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