求下式的积分
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∫(0->π/4) (secx)^3 dx
=∫(0->π/4) secx.dtanx
= [secx.tanx]|(0->π/4) - ∫(0->π/4) secx.(tanx)^2 dx
=√2 - ∫(0->π/4) secx.[(secx)^2- 1] dx
2∫(0->π/4) (secx)^3 dx =√2 + ∫(0->π/4) secx dx
∫(0->π/4) (secx)^3 dx
=(1/2) { √2 + [ln|secx+tanx|]|(0->π/4) }
=(1/2) [ √2 + ln(√2+1) ]
=∫(0->π/4) secx.dtanx
= [secx.tanx]|(0->π/4) - ∫(0->π/4) secx.(tanx)^2 dx
=√2 - ∫(0->π/4) secx.[(secx)^2- 1] dx
2∫(0->π/4) (secx)^3 dx =√2 + ∫(0->π/4) secx dx
∫(0->π/4) (secx)^3 dx
=(1/2) { √2 + [ln|secx+tanx|]|(0->π/4) }
=(1/2) [ √2 + ln(√2+1) ]
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