The value of -x2 - 1x4 - x2 - 1dx is

The correct option is B 1√(3)tan^ 1{x 1x√(3)} + C Let #160; I = ∫x^2 + 1x^4 + x^2 + 1dx = ∫ (1 + 1x^2 )x^2 + 1 + 1x^2 dx = ∫ (1 + 1x^2 ) ...

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Continuity of a Function

The value of ...

Question

The value of $\int \frac{(x^{2} + 1)}{x^{4} + x^{2} + 1} d x$ is

\frac{1}{\sqrt{3}} {tan}^{- 1} ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \frac{x - \frac{1}{x}}{\sqrt{3}} ⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭ + C

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\frac{1}{2 \sqrt{3}} log ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \frac{(x - \frac{1}{x}) - \sqrt{3}}{(x - \frac{1}{x}) + \sqrt{3}} ⎫ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎭ + C

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{tan}^{- 1} ⎛ ⎜ ⎜ ⎜ ⎝ \frac{x + \frac{1}{x}}{\sqrt{3}} ⎞ ⎟ ⎟ ⎟ ⎠ + C

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{tan}^{- 1} ⎛ ⎜ ⎜ ⎜ ⎝ \frac{x - \frac{1}{x}}{\sqrt{3}} ⎞ ⎟ ⎟ ⎟ ⎠ + C

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\int \frac{(x^{2} + 1) d x}{(x^{2} + 2) (2 x^{2} + 1)} = \frac{1}{3 \sqrt{(2)}} {{tan}^{- 1} \frac{x}{\sqrt{(2)}} + {tan}^{- 1} x \sqrt{2}} .

equals

A. x tan⁻¹ (x + 1) + C

B. tan^−
1 (x + 1) + C

C. (x + 1) tan⁻¹ x + C

D. tan⁻¹ x + C

\int \frac{e^{x} (x^{2} {tan}^{- 1} x + {tan}^{- 1} x + 1) d x}{x^{2} + 1}

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