Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\displaystyle\int{ \frac{ 1 }{ \log ( x ) } - \frac{ 1 }{ { \left( \log ( x ) \right) }^{ 2 } } }d x$$

Answer

$$1/log(x)-(d*x)/log(x)^2$$

Solution


Remove parentheses.
\[\int 1 \, \frac{d}{\log{x}}-\frac{1}{{\log{x}}^{2}}dx\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\int 1 \, \frac{d}{\log{x}}-\frac{1\times dx}{{\log{x}}^{2}}\]
Simplify  \(1\times dx\)  to  \(dx\).
\[\int 1 \, \frac{d}{\log{x}}-\frac{dx}{{\log{x}}^{2}}\]
Use this rule: \(\int a \, dx=ax+C\).
\[\frac{1}{\log{x}}-\frac{dx}{{\log{x}}^{2}}\]
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