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Indefinite Integrals question

2024 · 27 Jan · Shift 2 · Q47

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PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2024 · 27 Jan · Shift 2 · Q47

Indefinite Integrals question

2024 · 27 Jan · Shift 2 · Q47

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

\text { The integral } \int \frac{\left(x^8-x^2\right) \mathrm{d} x}{\left(x^{12}+3 x^6+1\right) \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)} \text { is equal to : }

A
$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^{1 / 3}+\mathrm{C}$
B
$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)+\mathrm{C}$
C
$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^{1 / 2}+\mathrm{C}$
D
$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^3+\mathrm{C}$

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