Mathematics

$$\displaystyle \int { \frac { 3x+1 }{ { \left( { 3x }^{ 2 }+2x+1 \right)  }^{ 3 } } dx } $$


SOLUTION
Let,  $$3x^2+2x+1=t$$

=>  $$(6x+2)dx=dt$$

=>  $$2(3x+1)dx=dt$$

So, given equation becomes,

=>  $$\int \dfrac{dt}{2t^3}$$

=>  $$-\dfrac{1}{8t^4} +C$$

=>  $$\dfrac{-1}{8(3x^2+2x+1)^4} +C$$
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Subjective Medium Published on 17th 09, 2020
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