Question

Solve the equation:-
$\int \frac{x^6+1}{x^2+1}dx$

Answer 1

Solve the equation

$\int \frac{x^6+1}{x^2+1}dx$

When degree of polynomial in numerator is higher then polynomial than first divide both the polynomial

$x^4-x^2+1x^2+1)\overline{x^6+1}{x}^6+x^4\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_-x^4+1-x^4-x^2\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_x^2+1x^2+1\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$=\int (x^4-x^2+1)dx$

$=\int x^{4}dx-\int x^{2}dx+\int dx$

$=\frac{x^5}{5}-\frac{x^3}{3}+x+c$