$ \int\left(\cos ^{-3 / 7} x\right)\left(\sin ^{-11 / 7} x\right) d x $ is equal to

Question

$ \int\left(\cos ^{-3 / 7} x\right)\left(\sin ^{-11 / 7} x\right) d x $ is equal to, $ \log \left|\sin ^{4 / 7} x\right|+c $, $ \frac{4}{7} \tan ^{4 / 7} x+c $, $ -\frac{7}{4} \tan ^{-4 / 7} x+c $, $ \log \left|\cos ^{3 / 7} x\right|+c $

MARKS App · Accepted Answer

∫ cos - 3 / 7 x sin - 11 / 7 x dx = ∫ sin - 11 / 7 x cos - 11 / 7 x . sec 2 x dx = ∫ tan - 11 / 7 x sec 2 x dx Put tan x = t ⇒ sec 2 x dx = dt ∴ I = ∫ t - 11 / 7 dt = - 7 4 tan - 4 / 7 x + c

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