If ∫cos3⁡xsin11⁡xdx=−2Atan−9/2⁡x+Btan−5/2⁡x+C  then 1A+1B is equal to

We observe that the sum of the exponents of cos x and sinx is32−112=−4=a ,negative even integer. So, we divide numerator and denominator by cos4 x∴I=∫cos3⁡xsin11⁡xdx=∫cos3/2⁡xsin11/2⁡xdx⇒I=∫cos3/2⁡x×cos4⁡xsin11/2⁡x×1cos4⁡xdx⇒I=∫1tan11/2⁡x1+tan2⁡xd(tan⁡x)⇒I=∫tan−11/2⁡x+tan−7/2⁡xd(tan⁡x)⇒I=−29tan−9/2⁡x−25tan−5/2⁡x+C⇒I=−219tan−9/2⁡x+15tan−5/2⁡x+CHence ,A=19 and B=15∴1A+1B=14