How do you find the indefinite integral of #int 10/x#?

2 Answers
VNVDVI
Feb 26, 2018

#10intdx/x=10ln|x|+C#

Explanation:

Factor #10# outside of the integral; this can be done as #10# is just a constant. Doing this cleans up the work a little, although it doesn't change the final answer.

#10intdx/x#

Recall that #intdx/x=ln|x|+C#.

First, note that we have the absolute value sign around #x# because #ln(x)# doesn't exist if #x# is negative. We want to avoid that. Furthermore, note that the natural log function is appropriate, because differentiating #ln(x)# gives us back #1/x,# the function we were originally trying to integrate. Finally, don't forget the constant of integration, #C#, as we must account for any possible constants (there are infinitely many -- the derivative of a constant is always #0#, #C# could be any value).

#10intdx/x=10ln|x|+C#

jonathan n.
Feb 26, 2018

#int10/x dx = 10ln(absx)+C#

Explanation:

#int10/xdx# can be converted and made simpler to #10int1/xdx#

#int1/xdx# is a basic integral, which equals #ln(absx)#

therefore, #int10/xdx = 10ln(absx)+C#

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