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原式=∫[0~π/2]x/[2cos²(x/2)]·dx
=∫[0~π/2]x/cos²(x/2)·d(x/2)
=∫[0~π/2]x·sec²(x/2)·d(x/2)
=∫[0~π/2]x·d[tan(x/2)]
=x·tan(x/2) |[0~π/2]
-∫[0~π/2]tan(x/2)·dx
=π/4-2∫[0~π/2]tan(x/2)·d(x/2)
=π/4+2ln[cos(x/2)] |[0~π/2]
=π/4-ln2
=∫[0~π/2]x/cos²(x/2)·d(x/2)
=∫[0~π/2]x·sec²(x/2)·d(x/2)
=∫[0~π/2]x·d[tan(x/2)]
=x·tan(x/2) |[0~π/2]
-∫[0~π/2]tan(x/2)·dx
=π/4-2∫[0~π/2]tan(x/2)·d(x/2)
=π/4+2ln[cos(x/2)] |[0~π/2]
=π/4-ln2
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