Question

How do we solve this?

Answer 1

`-(1)/(36\left(6x+1\right)^6) +C`

Explanation:

we're going to us u substitution

`\int (6x+1)^-7 dx`

`u=6x+1`

`\int(1)/(6u^7) du`

take out the constant,
`(1)/(6)`

`(1)/(6)` ·
`\int u^-7du`

next use the power rule,
`\int x^adx=(x^(a+1))/(a+1),\:\quad \:a\\e -1`

`(1)/(6)\cdot (u^(-7+1))/(-7+1)`

simplify by substituting
`6x+1` for
`u`

`(1)/(6)\cdot ((6x+1)^(-7+1))/(-7+1) = -(1)/(36\left(6x+1\right)^6)`

add a constant,
`C`

`-(1)/(36\left(6x+1\right)^6) +C`

Answer 2

`= - (1)/(36(6x + 1) ^(6) ) + c`

I hope I helped you^_^