若f(x)=e^2x则不定积分∫f(x/2)dx=?

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若f(x)=e^2x则不定积分∫f(x/2)dx=?
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若f(x)=e^2x则不定积分∫f(x/2)dx=?
若f(x)=e^2x则不定积分∫f(x/2)dx=?

若f(x)=e^2x则不定积分∫f(x/2)dx=?
令x/2 = u,x = 2u,dx = 2du
∫ f(x/2) dx
= ∫ f(u) · 2du
= 2∫ e^(2u) du
= ∫ e^(2u) d(2u)
= e^(2u) + C
= e^(2 · x/2) + C
= e^x + C

∫f(x/2)dx
=∫e^xdx
=e^x+C