Question

answer this question
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Answer 1

Step-by-step explanation:

$\huge\red{\underline{\underline{\bf Question:-}}}$

$\\ \\ \int \frac{ {x}^{3} }{x + 1}$

$\huge\red{\underline{\underline{\bf Answer:-}}}$

$\\ \\ \implies \int \frac{ {x}^{3} }{x + 1}dx \\ \\ \implies \int \frac{ {x}^{3} + 1 - 1 }{x + 1}dx \\ \\ \implies \int \frac{ {x}^{3} + 1}{x + 1} dx - \int \frac{1}{x + 1} dx \\ \\ \implies \int \frac{ \cancel{(x + 1)}( {x}^{2} - x + 1) }{ \cancel{x + 1}} dx - \int \frac{1}{x + 1} dx \\ \\ \implies \int {x}^{2} \: dx - \int x \: dx + \int dx - \int \frac{1}{x + 1} dx \\ \\ \implies \frac{ {x}^{3} }{3} - \frac{ {x}^{2} }{2} + x - ln(x + 1) +C \\ \\ \\ so \: \: your \: \: answer \: \: is \implies \\ \\ \huge \boxed{ \leadsto \frac{ {x}^{3} }{3} - \frac{ {x}^{2} }{2} + x - ln(x + 1) +C }$