`int (1 - 2x)^9 dx` Evaluate the indefinite integral.

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You need to evaluate the indefinite integral by performing the substitution 1 - 2x = t, such that:

`1 - 2x = t => -2dx = dt => dx = -(dt)/2`

`int (1-2x)^9dx = -1/2int t^9 dt `

You need to use the following formula of integration, such that:

`int t^n dt = (t^(n+1))/(n+1)`

`-1/2int t^9 dt = -(1/2)(t^(9+1))/(9+1) + c`

Replacing back 1 - 2x for t yields:

`int (1-2x)^9dx = -(1/2)((1-2x)^10)/10 + c`

Hence, evaluating the indefinite integral yields `int (1-2x)^9dx = -((1-2x)^10)/20 + c.`