Loading [MathJax]/jax/output/HTML-CSS/jax.js


1)

dxx(x4+1)=


A) 14log(x4+1x4)+C

B) 14log(x4x4+1)+C

C) 14log(x4+1)+C

D) 14log(x4x4+2)+C

Answer:

Option B

Explanation:

dxx(x4+1)=x4+1x4x(x4+1)dx

           =x4+1x(x4+1)dxx4x(x4+1)dx

     =1xdxx3x4+1dx

          =log|x|dxx3x4+1dx+C

 Let x4+1=tx3dx=dt

    x3dx=14

dx4(x4+1)=log|x|14dtt+C

 = log|x|14log|t|+C

=log|x|14log|x4+1|+C

   =14log|x4|14log|x4+1|+C

=14[log|x4|log|x4+1|+C

       =14log(x4x4+1)+C