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  4. ∫ ((x3+3x2+3x+1) /(x+1)5) dx =

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Q. $\int \frac {(x^3+3x^2+3x+1)} {(x+1)^5} dx $ =

KCETKCET 2006Integrals

Solution:

Let $ I=\int \frac{\left(x^{3}+3 x^{2}+3 x+1\right)}{(x+1)^{5}} d x $
$=\int \frac{(x+1)^{3}}{(x+1)^{5}} d x=\int \frac{1}{(x+1)^{2}} d x $
$=-\frac{1}{(x+1)}+c$