I dare you to have never thought of this question before

[logistic_guy]

Look at this simple integral.

\(\displaystyle \int 2^x \ dx = \frac{2^x}{\ln 2} + C\)

Why do we divide by \(\displaystyle \ln 2\)? From where did it come?

 

[khansaheb]

Look at this simple integral.

\(\displaystyle \int 2^x \ dx = \frac{2^x}{\ln 2} + C\)

Why do we divide by \(\displaystyle \ln 2\)? From where did it come?

Because

ln(2^x) = x*ln(x) ............ by extension of definition of ln(a) and ln(a*b)

 

[logistic_guy]

Because

ln(2^x) = x*ln(x) ............ by extension of definition of ln(a) and ln(a*b)

Thank you Sir khan.

 

[khansaheb]

Thank you Sir khan.

Correction:

ln(2^x) = x * ln(2)

 

[logistic_guy]

Correction:

ln(2^x) = x * ln(2)

Thank you again Sir khan.