`int (x^(2)+1)^(5//2)x dx` किसके बराबर है ?

Options

A. `(x^(2)+1)^(7//2)+C`
B. `(2)/(7)(x^(2)+1)^(7//2)`
C. `(1)/(7)(x^(2)+1)^(7//2)+C`
D. इनमे से कोई नहीं

Answer

C

Explanation

`I= int (x^(2)+1)^(5//2)*x dx`
माना `t=x^(2)+ 1 rArr dt=2xdx`
`:. I= int t^(5//2)(dt)/(2)=(1)/(2)[(t^(7//2))/(7//2)]+C`
`=(1)/(7)(x^(x)+1)^(7//2)+C`