If `intf(x)dx=g(x),then intx^(11)f(x^(6))dx` is equal to

Options

A. `1/6[x^(6)g(x^(6))-intx^(5)g(x^(6))]+C`
B. `1/6x^(6)g(x^(6))-intx^(5)g(x^(6))dx+C`
C. `1/6[x^(6)g(x^(6))-5intx^(5)g(x^(6))dx]+C`
D. None of these

Answer

2

Explanation

`I=intx^(11)f(x^(6))dx`
put `x^(6)=trArr6x^(5)dx=dt`
`I=1/6inttf(t)dt`
`=1/6[tg(t)-intg(t)dt]`
`=1/6[x^(6)g(x^(6))-intg(x^(6))d(x^(6))]`
`=1/6[x^(6)g(x^(6))-6intx^(5)g(x^(6))dx]`
`=1/6x^(6)g(x^(6))-intx^(5)g(x^(6))dx+C`