Question

$\int \frac{12x^3+8x}{x^4+1}dx=$

• A. $\log |x^4+1|+4{\tan }^{-1}\left(x^2\right)+c$
• B. $3\log |x^4+1|+4{\tan }^{-1}\left(x^2\right)+c$
• C. $3\log |x^4+1|+2{\tan }^{-1}\left(x^2\right)+c$
• D. $3\log |x^4+1|+8{\tan }^{-1}\left(x^2\right)+c$

Answer 1

The correct option is B $3\log |x^4+1|+4{\tan }^{-1}\left(x^2\right)+c$

$\int \frac{12x^3+8x}{x^4+1}dx$
$12\int \frac{x^3}{x^4+1}dx+\int \frac{8x}{x^4+1}dx$
$3\int \frac{d{x}^4}{x^4+1}+4\int \frac{d{x}^2}{x^4+1}$
$3log\mid x^4+1\mid +4{\tan }^{-1}\left(x^2\right)+c$
$=3log\mid x^4+1\mid +4{\tan }^{-1}\left(x^2\right)+c$