What is the integral `int dx/(5-3x)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The integral `int dx/(5 - 3x)` has to be determined.

This can be done using substitution.

Let `y= 5 - 3x`

Differentiating both the sides with respect to x gives:

`dy/dx = -3`

`=> dx = -(dy)/3`

Substituting for 5 - 3x and dx in the original integral gives:

`int dx/(5 - 3x)`

= `-(1/3) int dy/y`

= `-(1/3)*ln y`

As y = 5 - 3x, the integral is:

`-(1/3)*ln (5 - 3x)`

The integral `int dx/(5 - 3x) = -(1/3)*ln (5 - 3x)`

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