Function Expression :
\[f(x)=sin(x ). e^x \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = \left\langle -\infty, +\infty\right\rangle \]
\[ \]
Derivate
\[f^{\,\prime}(x)=e^{x} \sin{\left(x \right)} + e^{x} \cos{\left(x \right)} \]\[f^{\,\prime}(x)=\sqrt{2} e^{x} \sin{\left(x + \frac{\pi}{4} \right)} \]
\[ \]
Integral
\[F(x) = \frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2} \]Sign Table
Variation Table
Plot
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