Mathematics

The value of $$\displaystyle \int \dfrac {3x+5}{3x^2+10x+6}  \ dx$$ is


SOLUTION
Let 
$$3x^2+10x+6=t$$

$$6x+10dx=dt$$...........$$(differentiating \  with \  respect \  to \  x)$$

$$2(3x+5)=\dfrac {dt} {dx}$$

$$\displaystyle \int \dfrac 12 \cdot \dfrac 1tdt$$

$$=\dfrac 12\log t+c$$

$$=\dfrac 12\log(3x^2+10x+6)+c$$
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Subjective Medium Published on 17th 09, 2020
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