`int 7/(z-10)^7 dz` Find the indefinite integral

`int 7/(z-10)^7 dz`

To solve, apply u-substitution method.

`u=z-10`

`du=dz`

Expressing the integral in terms of u, it becomes

`= int 7/u^7 du`

Then, apply the negative exponent rule `a^(-m)=1/a^m` .

`= int 7u^(-7)du`

`=7int u^(-7)du`

To take the integral of this, apply the formula `int x^ndx=x^(n+1)/(n+1)+C` .

`= 7 *u^(-6)/(-6) +C`

`=-7/(6u^6)+C`

And substitute back `u=z-10`

`=-7/(6(z-10)^6) +C`

Therefore, `int 7/(z-10)^7 dz==-7/(6(z-10)^6) +C` .

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