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Question Number 85648 by sakeefhasan05@gmail.com last updated on 23/Mar/20

$$\int \frac{({\mathrm{x}}^3-4)}{(\mathrm{x}+1)}\mathrm{dx}$$

Answered by petrochengula last updated on 23/Mar/20

$$=\int \frac{x^3+1-5}{(x+1)}dx$$$$=\int \frac{x^3+1}{x+1}dx-5\int \frac{1}{x+1}dx$$$$=\int \frac{(x+1)(x^2-x+1)}{x+1}dx-5ln\mid x+1\mid +C$$$$=\frac{x^3}{3}-\frac{x^2}{2}+x-5ln\mid x+1\mid +C$$$$$$

Answered by petrochengula last updated on 23/Mar/20

$$=\int \frac{x^3+1-5}{(x+1)}dx$$$$=\int \frac{x^3+1}{x+1}dx-5\int \frac{1}{x+1}dx$$$$=\int \frac{(x+1)(x^2-x+1)}{x+1}dx-5ln\mid x+1\mid +C$$$$=\frac{x^3}{3}-\frac{x^2}{2}+x-5ln\mid x+1\mid +C$$$$$$

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