1)
[tex]f(x)= a^{x}*e^{x} \\ f(x)=(a*e)^{x} \\ \int { (a*e)^{x} } \, dx = \frac{ (a*e)^{x} }{ln(a*x)}=\frac{ a^{x}*e^{x} }{ln(a)+ln(e)}=\frac{ a^{x}*e^{x} }{ln(a)+1} \\ Conditii: a >0 ..si.. a \neq 1 [/tex]
2)
[tex]f(x)= 2^{x}*e^{x} \\ f(x)=(2*e)^{x} \\ \int { (2*e)^{x} } \, dx = \frac{ (2*e)^{x} }{ln(2*x)}=\frac{ 2^{x}*e^{x} }{ln(2)+ln(e)}=\frac{ 2^{x}*e^{x} }{ln(2)+1} [/tex]
Am folosit formulele:
[tex] 1) \\ a^{c} * b^{c} = (ab)^{c} ..din ..proprietatile.. puterilor \\ \\ 2) \\ \int { a^{x} } \, dx = \frac{ a^{x} }{ln(a)} [/tex]
Conditii: a ∈ R*+ \ {1}
