Question

If curve $f(x)=\int x^{11}{\left(2x^3+3x+4\right)}^3\left(1+x+x^3\right)dx$ passes through origin & $f(1)=\frac{p}{q}$ where $p\&q$ are relatively prime then $p-q$ is

Answer 1

Answer: 2171

$f(x)=\int x^{11}{\left(2x^3+3x+4\right)}^3\left(1+x+x^3\right)dx$
$2x^6+3x^4+4x^3=t$
$f(x)=\frac{1}{48}{\left(2x^6+3x^4+4x^3\right)}^4$
$f(1)=\frac{9^4}{48}=\frac{2187}{16}=\frac{p}{q}$
$\therefore p-q=2171$