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If $\int \tan^{4} x d x = K \tan^{3} x + L \tan x + f (x)$ , then

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K=2/3

L=−2

f(x)=x+C

K=4/3

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detailed solution

Correct option is C

∫tan4⁡xdx=∫tan2⁡xsec2⁡x−1dx=tan3⁡x3−∫sec2⁡x−1dx=tan2⁡x3−tan⁡x+x+C.

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If ∫tan4⁡xdx=Ktan3⁡x+Ltan⁡x+f(x), then

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If $\int \tan^{4} x d x = K \tan^{3} x + L \tan x + f (x)$ , then