Question

∫_ln2^ln4▒〖(e^(x+1)+1)dx〗 ∫_e^(e^4)▒〖(2x+3)/x dx〗?

Answer 1

更新1:

1.∫_ln2^ln4▒〖(e^(x+1)+1)dx〗 2.∫_e^(e^4)▒〖(2x+3)/x dx〗

(1) u=x+1
du=dx ∫(e^(x+1)+1)dx =∫(e^u+1)du=e^u+u=e^(x+1)+x+1 ∫_ln2^ln4 (e^(x+1)+1)dx = [e^(x+1)+x+1]_ln2^ln4 =log(4)-log(2)+2e =log(2)+2e (2) ∫(2x+3)/x dx=∫(2+3/x) =2x+3log(x) ∫_e^(e^4)(2x+3)/x dx =(2x+3)/x]_e^(e^4) =2e^4-2e+3(log(e^4)-log(e)) =2e^4-2e+3(4-1) =2e^4-2e+9