Question

\[\int\frac{6x - 5}{\sqrt{3 x^2 - 5x + 1}} \text{ dx }\]

Answer 1

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