Question

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

• A. $Ta{n}^{-1}x+c$
• B. $Log(x+1)+c$
• C. $\frac{1}{5}Log(x+1)+c$
• D. $-\frac{1}{(x+1)}+c$

Answer 1

Answer: (D)

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