Question

$\int \frac{x^3dx}{1+x^4}$ equals

• A. $log (x^4+1) +C$
• B. $\frac{1}{4} log (x^4+1)+C$
• C. $\frac{1}{2} log (x^4 +1) +C$
• D. $None\, of\, these$

Answer 1

Answer: (A)

$log (x^4+1) +C$

Answer 2

Let $I = \int \frac{x^3}{1+x^4} dx \,\,...(i)$
Again, let $1 + x^4 = t$
$\Rightarrow 4x^3 \,dx = dt$
$\Rightarrow x^3 \,dx = \frac{1}{4} dt$
On putting these values in E $(i)$, we get
$I = \frac{1}{4} \int \frac{dt}{t}$
$=\frac{1}{4} log \,t +C$
$\Rightarrow I = \frac{1}{4} log (1 + x^2) + C$ [From E $(i)$]