请问这个积分怎么算啊
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∫(0->π/4) dx/(cosx)^3
=∫(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 -∫(0->π/4) secx dx]
=(1/2) {√2 - [ln|secx+tanx| ]|(0->π/4) }
=(1/2) [√2 - ln√2 ]
=(1/2)√2 -(1/4)ln2
=>
∫(0->π/4) dx/(cosx)^3 =(1/2)√2 -(1/4)ln2
=∫(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 -∫(0->π/4) secx dx]
=(1/2) {√2 - [ln|secx+tanx| ]|(0->π/4) }
=(1/2) [√2 - ln√2 ]
=(1/2)√2 -(1/4)ln2
=>
∫(0->π/4) dx/(cosx)^3 =(1/2)√2 -(1/4)ln2
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