Question

Evaluate :

$\int \frac{x^4}{x^2+1}dx$

• A. $\frac{x^3}{3}-x+{\tan }^{-1}x+C$
• B. $\frac{x^3}{3}+{\tan }^{-1}x+C$
• C. $x+{\tan }^{-1}x+C$
• D. none of these

Answer 1

The correct option is A $\frac{x^3}{3}-x+{\tan }^{-1}x+C$

$I=\int \frac{x^4}{x^2+1}dx$

$I=\int \frac{x^4-1+1}{x^2+1}dx$

$I=\int \frac{x^4-1}{x^2+1}dx+\int \frac{1}{x^2+1}dx$

$I=\int (x^2+1)dx+\int \frac{1}{x^2+1}dx$

$I=\frac{x^3}{3}-x+{\tan }^{-1}x+C$