Let x be a continuous variable defined over the interval (-∞, ∞) and \(f\left( x \right) = {e^{ - x - {e^{ - x}}}}\). The integral \(g\left( x \right) = \smallint f\left( x \right)dx\) is equal to
\({e^{ - {e^{ - x}}}}\)
Differentiate e^(−e^(−x)): its derivative is e^(−e^(−x))e^(−x)=e^(−x−e^(−x)). Thus an antiderivative is e^(−e^(−x)); the general indefinite integral also includes an arbitrary additive constant.
Important Questions from Indefinite Integrals
- What is \(U(x)\,V(x)\) equal to?
$X^4 + C$ is the general integral of
What is \(\rm \int \frac{dx}{x(x^2 + 1)}\) equal to?
If \(\rm \int \sqrt{1 - sin 2x} \space dx\) = A sinx + B cosx + C, where 0 < x < \(\frac{\pi}{4}\) , then which one of the following is correct?
What is \(\smallint {{\rm{e}}^{\sin {\rm{x}}}}\left( {\frac{{{\rm{x}}{{\cos }^3}{\rm{x}} - \sin {\rm{x}}}}{{{{\cos }^2}{\rm{x}}}}} \right){\rm{dx}}\) equal to?
