Mathematics › Indefinite Integration › Integration using Reduction Formula
Given In=∫0π4tannxdxIn+In+2=∫0π4tannxdx+∫0π4tann+2xdx=∫0π4tannxsec2xdx=∫01tndt where tanx=t=tn+1n+101=1n+1Now, 1I2+14+1I3+I5+1I4+16=3+4+5=12=1I11+I13
Given In=∫0π4tannxdx
In+In+2=∫0π4tannxdx+∫0π4tann+2xdx
=∫0π4tannxsec2xdx
=∫01tndt where tanx=t
=tn+1n+101=1n+1
Now, 1I2+14+1I3+I5+1I4+16=3+4+5=12
=1I11+I13
Asked in: AP EAMCET 2022 (04 Jul Shift 2)
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