Question

integrala din e la x + e la -x dx​

Answer 1

∞Răspuns:

∫(eˣ+e⁻ˣ)dx

∫eˣdx=eˣ

∫e⁻ˣdx=-e⁻ˣ

∫(eˣ+e⁻ˣ)=eˣ-e⁻ˣ+c

Explicație pas cu pas:

∫

Answer 2

$\int (e^x+e^{-x}) \,dx=\\\int e^x\,dx+\int e^{-x}\,dx=\\e^x+(-e^{-x})+C=\\e^x-e^{-x}+C\\\\\frac{d\,e^x}{d\,x}=e^x\\\\\frac{d\,e^{-x}}{d\,x}=\frac{d\,e^{f(x)}}{d\,x}, \text{unde f(x)=-x}\\\\\frac{d\,e^{f(x)}}{d\,x}=e^{f(x)}\times \frac{d\,f(x)}{d\,x}=e^{-x}\times\frac{d\,(-x)}{d\,x}=e^{-x}\times(-1)=-e^{-x}\\\\\implies -\frac{d\,e^{-x}}{d\,x}=e^{-x}\implies \\\\\int e^{-x}\,dx=\int -\frac{d\,e^{-x}}{d\,x}\,dx=-e^{-x}+C$