Question

求∫2的x次方e的x次方dx=?

Answer 1

∫(2^x)(e^x)dx=∫e^(xln2) e^xdx=∫e^(xln2 + x)dx=(1/(ln2+1))∫e^((ln2+1)x)d(ln2+1)x

=e^((ln2+1)x) / (ln2+1) + C

=(2^x)(e^x) / (ln2+1) + C