the given expression is,
[tex]\int \frac{x}{(7x^2+3)^5}dx[/tex]
take P = 7x^2 + 3
differentiate the function,
[tex]\begin{gathered} dp=14x\times dx \\ xdx=\frac{dp}{14} \end{gathered}[/tex]
put the values.,
[tex]\int \frac{1}{14}\frac{dp}{p^5}[/tex][tex]\begin{gathered} =\frac{1}{14}\int \frac{dp}{p^5} \\ =\frac{1}{14}\times\frac{P^{-5+1}}{-5+1}+C \end{gathered}[/tex][tex]\begin{gathered} =\frac{1}{14}\times\frac{1}{-4}P^{-4}+C \\ =-\frac{1}{56}P^{-4}+C \end{gathered}[/tex]
now put the value of P = 7x^2 + 3
[tex]=-\frac{1}{56}(7x^2+3)^{-4}+C[/tex]
thus, the correct answer is option A
