Question

If $\int x^{23}(1-x{)}^{31}(3-7x)dx=\frac{x^p(1-x{)}^q}{r}+C$ where $p,q,r\in N$ and $C$ is integration constant then H.C.F. of $(p,q,r)$ is

• A. 8
• B. 4
• C. 2
• D. 1

Answer 1

Answer: (A)

$x^{23}(1-x{)}^{31}(3-7x)=x^{23}(1-x{)}^{31}[3(1-x)-4x]$
$=3x^{23}(1-x{)}^{32}-4x^{24}(1-x{)}^{31}$
$=\frac{1}{8}\cdot \frac{d}{dx}\left(x^{24}(1-x{)}^{32}\right)$