[INTEGRAL] S3^x.e^xdx= ?

Question

[INTEGRAL] S3^x.e^xdx= ? thanks guys

Answer 1

∫3^xe^x dx

 

3^x = e^{ln3^x} = e^xln3               [Identity: ln(a^b) = b*ln(a)]

 

∫e^xln3e^x dx = ∫e^(1+ln3)x dx

 

Can you finish it from here?  Remember, (1+ln3) is just a constant.  Let u = (1+ln3)x, du = (1+ln3)dx.