Question

$solve\ratio - ∫ \frac{ {x}^{3} + 4 {x}^{2} - 7x + 5 }{x + 2} dx$​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\displaystyle\rm{\int\dfrac{{x}^{3}+4{x}^{2}-7{x}+5}{x+2}\,dx}$

$\displaystyle\rm{=\int\dfrac{{x}^{3}+2{x}^{2}+2{x}^{2}+4{x}-11{x}-22+27}{x+2}\,dx}$

$\displaystyle\rm{=\int\dfrac{{x}^{2}(x+2)+2{x}(x+2)-11(x+2)+27}{x+2}\,dx}$

$\displaystyle\rm{=\int\dfrac{\left({x}^{2}+2{x}-11\right)(x+2)+27}{x+2}\,dx}$

$\displaystyle\rm{=\int\left({x}^{2}+2{x}-11\right)dx+\int\dfrac{27}{x+2}\,dx}$

$\displaystyle\rm{=\dfrac{{x}^{3}}{3}+2\cdot\dfrac{{x}^{2}}{2}-11x+27\cdot\ln|x+2|+C}$

$\displaystyle\rm{=\dfrac{{x}^{3}}{3}+{x}^{2}-11x+27\cdot\ln|x+2|+C}$

Answer 2

answer deleted

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