Question

$\int \frac{5x^2+4n-1}{\sqrt{n^2-4n+5}}dx$

Answer 1

We have,

$\int \frac{5x^2+4n-1}{\sqrt{n^2-4n+5}}dx$

$\Rightarrow \int \frac{5x^2}{\sqrt{n^2-4n+5}}dx+\int \frac{4n-1}{\sqrt{n^2-4n+5}}dx$

$\Rightarrow \frac{5}{\sqrt{n^2-4n+5}}\int x^{2}dx+\frac{4n-1}{\sqrt{n^2-4n+5}}\int 1dx$

$\Rightarrow \frac{5x^3}{3\sqrt{n^2-4n+5}}+\frac{4n-1}{\sqrt{n^2-4n+5}}x+C$

Hence, this is the answer.