Question

Integration of ( x^6-1/x^2+1) ×dx​

Answer 1

Answer:

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

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

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

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

$\int \sf \frac{(x^2)^3 + 1^3} {x^2+1} dx$ - $\int \sf \frac{2} {x^2+1} dx$

$\int \sf \frac{(x^2+1) (x^4-x^2+1)} {x^2+1} dx$ - $2 \int \sf \frac{1}{x^2+1} dx$

$\int \sf{(x^4-x^2+1)} dx$ - $2 \sf{tan^{-1} x}$

$\int \sf{x^4} dx$ - $\int \sf{x^2} dx$ + $\int \sf{1} dx$ - $2 \sf{tan^{-1} x}$

$\sf \frac{x^5}{5}$ - $\sf \frac{x^3}{3}$ + $\sf{x} - 2 \sf{tan^{-1} x}$ + C