Question

帮忙求一道简单的不定积分∫{2^x[e^(3x)+1]}/(e^x+1)dx帮忙解一下!请问一下=∫{t^(ln2-1)

Answer 1

将2^x写成e^(xlns)=(e^x)^ln2,设e^x=t,则dt=tdx

从而原积分

∫{2^x[e^(3x)+1]}/(e^x+1)dx

=∫{t^ln2*[t^3+1]}/(t+1)dx

=∫{t^(ln2-1)*[t^3+1]}/(t+1)dt

=∫{t^ln2*(t^2-t+1)dt

=∫[t^(ln2+2)-t^(ln2+1)-t^ln2]dt

接下来会算了吧,然后再把t=e^x带入就行了.