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what is the integral 1/x

 Mar 4, 2015

Best Answer 

 #2
avatar+26364 
+5

What is the integral 1/x ?

$$\small{\text{
We substitute : $ x = e^u \qquad \ dx = e^u\ du
$
}}\\
\small{\text{
$\int {\frac{1}{x} }\ dx = \int{\frac{1}{e^u} }\cdot e^u \ du = \int{1}\ du = u
$
}}\\\\
\small{\text{Back substitute :
$\int {\frac{1}{x} }\ dx = u \qquad u = \ln{(x)}
$
}}\\
\small{\text{
$\int {\frac{1}{x} }\ dx = \ln{(x)} + c
$
}}$$

 Mar 5, 2015
 #1
avatar+33603 
+5

$$\int\frac{1}{x}dx=ln(x)+c$$

 

ln is log to the base e and c is a constant.

.

 Mar 4, 2015
 #2
avatar+26364 
+5
Best Answer

What is the integral 1/x ?

$$\small{\text{
We substitute : $ x = e^u \qquad \ dx = e^u\ du
$
}}\\
\small{\text{
$\int {\frac{1}{x} }\ dx = \int{\frac{1}{e^u} }\cdot e^u \ du = \int{1}\ du = u
$
}}\\\\
\small{\text{Back substitute :
$\int {\frac{1}{x} }\ dx = u \qquad u = \ln{(x)}
$
}}\\
\small{\text{
$\int {\frac{1}{x} }\ dx = \ln{(x)} + c
$
}}$$

heureka Mar 5, 2015

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