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 (x)/((7x^2+3)^5)dx`

take P = 7x^2 + 3

differentiate the function,

`\begin{gathered} dp=14x* dx \\ xdx=(dp)/(14) \end{gathered}`

put the values.,

`\int (1)/(14)(dp)/(p^5)`
`\begin{gathered} =(1)/(14)\int (dp)/(p^5) \\ =(1)/(14)*(P^(-5+1))/(-5+1)+C \end{gathered}`
`\begin{gathered} =(1)/(14)*(1)/(-4)P^(-4)+C \\ =-(1)/(56)P^(-4)+C \end{gathered}`

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

`=-(1)/(56)(7x^2+3)^(-4)+C`

thus, the correct answer is option A