# How do you use Integration by Substitution to find #intdx/(5-3x)#?

##### 1 Answer

Jul 25, 2014

The answer is

#-1/3*ln(5-3x)+c# , where c is constant

**Solution**

For problems like

#int dx/(a+bx)# ,

we start with assuming

then, differentiating this assumption

#dx=(du)/b#

Now, substituting this in problem,

#int(du)/(b*u) = 1/b*lnu +c# , where c is constant

now, substituting u in the solution,

#1/b*ln(a+bx)+c#

Similarly following for the problem,

let

then,

now substituting in the problem, we get

#int-1/3*(du)/u = -1/3*ln(u)+c#

Finally, plugging in u, the answer will be