Exponentially Powerful Integral

Calculus Level 3

If $\displaystyle S = \int_3^{27} \dfrac n{n^2 + 1} \, dn$ , find $e^{4S }$ .

The answer is 5329.

1 solution

Rishabh Jain
Feb 13, 2016

$\Large \mathcal{S}= \dfrac{1}{2} \int_{3}^{27} \dfrac{d(n^2+1)}{n^2+1}$ $\Large =\dfrac{1}{2}( \ln (n^2+1)|_{\small{3}}^{\small{27}})$ $\Large =\dfrac{1}{2}(\ln (73))$ $\Large \therefore e^{4\mathcal{S}}=e^{2\ln 73}=e^{\ln (73)^2}=73^2~~~$ $~~~~~~=\huge\boxed{\color{#007fff}{5329}}$

${ e }^{ { \ln { 73 } }^{ 2 } }\neq { \left( { e }^{ ln73 } \right) }^{ 2 }\\=5329$

Please do the amends

Joel Yip - 5 years, 4 months ago

So what I have to correct?? Or correction made??

Rishabh Jain - 5 years, 3 months ago

change it to ${ \left( { e }^{ ln73 } \right) }^{ 2 }$