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Wanted to know if anyone could explain why if you simplify an expression into a different equivalent form, the integrations are different depending on which form you use.

For example:

[itex]\frac{1}{\frac{5x}{7}+3}[/itex] = [itex]\frac{1}{\frac{5}{7}(x+4.2)}[/itex]

[itex]\int[/itex][itex]\frac{1}{\frac{5x}{7}+3}[/itex]dx = [itex]\frac{7}{5}[/itex]ln([itex]\frac{5x}{7}[/itex]+3)

while

[itex]\int[/itex][itex]\frac{1}{\frac{5}{7}(x+4.2)}[/itex]dx = [itex]\frac{7}{5}[/itex]ln(x+4.2)

The two integrations are not equal despite having integrated two equivalent expressions. The issue is if I had to integrate [itex]\frac{1}{\frac{5x}{7}+3}[/itex] I would simplify it to

[itex]\frac{1}{\frac{5}{7}(x+4.2)}[/itex] which gives a different integration than the original expression.

Thanks for any input

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# Simplifying changes integration

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