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Question

If In=π40tannx dx, then 1I3+I5 is equal to

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Solution

In=π40tannx dx
For n2,nI, we can write
I=π40(sec2x1)tann2x dxI=[tann1xn1]π40π40tann2xdxIn=1n1In2

Now, putting n=5, we get
I5=14I3I3+I5=141I3+I5=4

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