Question

그는 [d (7x2 + 37 0) 를 0 (24 3) 4 10 ○ (7x2+3) 4+c ○ (x3)6+c 급 (7x + 3) 6 5

Answer 1

the given expression is,

$\int \frac{x}{(7x^2+3)^5}dx$

take P = 7x^2 + 3

differentiate the function,

$\begin{gathered} dp=14x\times dx \\ xdx=\frac{dp}{14} \end{gathered}$

put the values.,

$\int \frac{1}{14}\frac{dp}{p^5}$$\begin{gathered} =\frac{1}{14}\int \frac{dp}{p^5} \\ =\frac{1}{14}\times\frac{P^{-5+1}}{-5+1}+C \end{gathered}$$\begin{gathered} =\frac{1}{14}\times\frac{1}{-4}P^{-4}+C \\ =-\frac{1}{56}P^{-4}+C \end{gathered}$

now put the value of P = 7x^2 + 3

$=-\frac{1}{56}(7x^2+3)^{-4}+C$

thus, the correct answer is option A