Mathematics

$$\displaystyle \int \dfrac{x^3}{x + 1}$$ is equal to


ANSWER

$$x - \dfrac{x^2}{2} - \dfrac{x^3}{3} - log |1 + x| + C$$


SOLUTION
Let $$I = \displaystyle \int \dfrac{x^3}{x + 1}dx$$
$$= \displaystyle \int \dfrac{(x^3+1)-1}{x + 1}dx$$
$$= \displaystyle \int \left ( (x^2 - x + 1) - \dfrac{1}{(x + 1)} \right ) dx$$
$$= \dfrac{x^3}{3} - \dfrac{x^2}{2} + x - log | x + 1| + C$$
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Single Correct Medium Published on 17th 09, 2020
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