We have, I=∫6x 13x^2 x+6dx #160; #160; #160; #160; #160; #160; #8230; #8230;. (1) #160;Let t=3x^2 x+6 dt=( 6x 1 )dx #16 ...

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Solving Linear Differential Equations of First Order

Solve ∫6x-1...

Question

Solve $\int \frac{6 x - 1}{3 x^{2} - x + 6} d x$

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Solution

We have,

$I = \int \frac{6 x - 1}{3 x^{2} - x + 6} d x$ ……. (1)

Let $t = 3 x^{2} - x + 6$

$d t = (6 x - 1) d x$

Therefore,

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

$I = ln (t) + C$

On putting the value of $t$ , we get

$I = ln (3 x^{2} - x + 6) + C$

Hence, this is the answer,

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