int frac{x^3}{(x+1)^2} ,dx= | vedclass

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Question

$	ext{ધારો કે } I = \int \frac{x^3}{(x+1)^2} \, dx$
$u = x+1 \Rightarrow x = u-1, \quad dx = du$
$I = \int \frac{(u-1)^3}{u^2} \, du = \int \frac{u

Vedclass · Accepted Answer

$\frac{x^2}{2}-2x+3\log|x+1|+\frac{1}{x+1}+c$

Vedclass · Answer

$	ext{ધારો કે } I = \int \frac{x^3}{(x+1)^2} \, dx$
$u = x+1 \Rightarrow x = u-1, \quad dx = du$
$I = \int \frac{(u-1)^3}{u^2} \, du = \int \frac{u^3 - 3u^2 + 3u - 1}{u^2} \, du$
$I = \int \left(u - 3 + \frac{3}{u} - \frac{1}{u^2}ight) du$
$	ext{દરેક પદનું સંકલન કરતા:}$
$I = \frac{u^2}{2} - 3u + 3\log|u| + \frac{1}{u} + C$
$u = x+1 	ext{ મૂક્તા:}$
$I = \frac{(x+1)^2}{2} - 3(x+1) + 3\log|x+1| + \frac{1}{x+1} + C$
$I = \frac{x^2 + 2x + 1}{2} - 3x - 3 + 3\log|x+1| + \frac{1}{x+1} + C$
$I = \frac{x^2}{2} - 2x + 3\log|x+1| + \frac{1}{x+1} + C$
$	ext{આમ, સાચો વિકલ્પ } A 	ext{ છે.}$

$\int \frac{x^3}{(x+1)^2} \,dx=$

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