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\(\begin{equation} \begin{aligned} & f(x)=7(\tan x)^8+7(\tan x)^6-3(\tan x)^4-3\left(\tan ^2 x\right) \\ & I_1=\…

Q1

\(\begin{equation}
\begin{aligned}
& f(x)=7(\tan x)^8+7(\tan x)^6-3(\tan x)^4-3\left(\tan ^2 x\right) \\
& I_1=\int f(x) d x, I_2= \int x f(x) d x \\
& 7 I_1+12 I_2=
\end{aligned}
\end{equation}\)

[Jee Main 2025]

a

\(\left(12x+7\right)\left({\tan }^{7}x-{\tan }^{3}x\right)+{\tan }^{4}x\left(3-2{\tan }^{2}x\right)+c\)

b

\(\left(12x+7\right)\left({\tan }^{7}x-{\tan }^{3}x\right)-{\tan }^{4}x\left(3-{\tan }^{2}x\right)+c\)

c

\(\left(12x-7\right)\left({\tan }^{7}x-{\tan }^{3}x\right)+{\tan }^{4}x\left(3-2{\tan }^{2}x\right)+c\)

d

None of these

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