Mathematics

# Evaluate: $\displaystyle \int{\dfrac{{x}^{3}}{x+2}dx}$

##### SOLUTION
$\int \frac{x^{3}dx}{x+2} = \int \frac{(x^{3}+8-8)dx}{x+2}$
$=\int \frac{(x^{3}+8)dx}{(x+2)} - \int \frac{8dx}{x+2}$
$=\int \frac{(x+2)(x^{2}-2x+4)dx}{(x+2)} -8 \int \frac{dx}{x+2}$
$= \int (x^{2}-2x+4)dx - 8 \int \frac{dx}{x+2}$
$= \frac{x^{3}}{3}-\frac{2x^{2}}{2}+4x-8log |x+2|+c$
$= \frac{x^{3}}{3} -x^{2}+4x-8 log |x+2| +c$
Where c is the constant of integration

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

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Evaluate $\int {{e^3}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
What is $\int \dfrac {dx}{\sqrt {x^{2} - a^{2}}}$ equal to?
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Q5 Single Correct Hard

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