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`int14(x-5)^6 dx` Find the indefinite integral

`int14(x-5)^6dx`


To solve, apply u-substitution method.



`u=x-5`


`du=dx`



Expressing the integral in terms of u, it becomes


`=int 14u^6 du`


`=14int u^6du`


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


`=14*u^7/7 + C`


`=2u^7+C`


And substitute back u = x-5.


`=2(x-5)^7+C`


Therefore, `int 14(x-5)^6dx=2(x-5)^7+C` .

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