Mathematics

Integrate $$\displaystyle\int \dfrac{(5x^2+7x+3)}{(x+1)}dx$$


SOLUTION
$$\int { \dfrac { { 5x }^{ 2 }+7x+3 }{ x+1 }  } dx$$
$$\int { \dfrac { { 5x }^{ 2 }+5x+2x+2+1 }{ x+1 }  } dx$$
$$=\int { \dfrac { { 5x }^{ 2 }+5x }{ x+1 } dx } +\int { \dfrac { 2x+2 }{ x+1 } dx } +\int { \dfrac { 1 }{ x+1 } dx } $$
$$=\int { 5xdx } +\int { 2dx } +\int { \dfrac { 1 }{ x+1 } dx } $$
$$=\dfrac { { 5x }^{ 2 } }{ 2 } +2x+ln\left| x+1 \right| +C$$
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Subjective Medium Published on 17th 09, 2020
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