Question

integration dx/3x^2+13x-10
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Answer 1

Step-by-step explanation:

We have,

$\int \frac{dx}{3 {x}^{2} + 13x - 10}$

$= \int \frac{dx}{3 {x}^{2} + 15x - 2x - 10 }$

$= \int \frac{dx}{3x(x + 5) - 2(x + 5)}$

$= \int \frac{dx}{(x + 5)(3x - 2)}$

$= - \int \frac{dx}{17(x + 5)} + \int \frac{3dx}{17(3x - 2)}$

$= - \frac{1}{17} ln(x + 5) + \frac{1}{17} ln(3x - 2) + c$

$= \frac{1}{17} ln( \frac{ 3x - 2 }{x + 5} ) + c$