L [t^2 − e^−2t + cosh^2 3t]
You asked:
Evaluate the expression: \(L \cdot \left({t}^{2} - {e}^{-2} \cdot t + {\cosh\left( 3 t \right)}^{2}\right)\)
MathBot Answer:
Evaluated
\(\displaystyle L \cdot \left({t}^{2} - {e}^{-2} \cdot t + {\cosh\left( 3 t \right)}^{2}\right) = L \left(t^{2} - \frac{t}{e^{2}} + \cosh^{2}{\left(3 t \right)}\right) \)
Expanded
\[L \cdot \left({t}^{2} - {e}^{-2} \cdot t + {\cosh\left( 3 t \right)}^{2}\right) = t^{2} L - \frac{L t}{e^{2}} + L \cosh^{2}{\left(3 t \right)}\]
Factored
\[L \cdot \left({t}^{2} - {e}^{-2} \cdot t + {\cosh\left( 3 t \right)}^{2}\right) = \frac{L \left(t^{2} e^{2} - t + e^{2} \cosh^{2}{\left(3 t \right)}\right)}{e^{2}}\]
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).