How can we get the result of ∫ (upper Π / 4 lower 0) tanxdx = lncosx I (upper Π / 4 lower 0)?

You change Tan x to sin X / cos X
Then SiN x DX is reduced to D (COS x)
There is an integral sign on the right: 1 / cos x D (COS x)
Use the formula to get your conclusion

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